mk1980

it flips because the center of lift (blue/black indicator) is in front of the center of mass (yellow/black indicator) you can try to move the wings further back so the CoL ends up behind the CoM

you overlooked the "5" in front of both numbers. it's ~5760km AP and ~5180km PE. in other words your orbit is supposed to look like the orange target orbit displayed by the game. you can actually ignore the numbers in the contract description and just eyeball it based on the displayed target orbit.

the AN and DN nodes mark the intersection between your orbital plane and the plane of the requested orbit. the game only draws them on the target orbit line and not on your current orbit. if the angle between the planes is 0, you don't have to change your inclination. you put a simple prograde maneuver at your AP that raises the PE to roughly the required 5000 km and add some radial or anti radial to (roughly) line up the AP and PE with the locations of the 2 nodes on the target orbit. you usually don't have to be super accurate. the contracts are fairly generous

in my experience large planes are much easier to balance if you move the engines (and main wings) from the back to the center of the plane. basically like the concept of the real life "Skylon" SSTO project. you'll have your cockpit and passenger cabin in the front and the fuel tanks along the fuselage, with engines and wings roughly in the center. so the CoM will gradually shift a bit forward as the tanks run dry. which makes it easier to keep the plane flying straight.

if you unlocked the mammoth and the mainsail, you should also have the kickback and thumper SRBs. and probably also the recently added 2.5m monsters (haven't memorized their names yet) if you don't have those, you should probably check if your installation is broken.

depends on the goal of the design. getting kerbals to LKO is trivial at this stage in the tech tree. the only pragmatic reason why you'd even want to use an SSTO plane rather than a simple disposable rocket is to save some money. to realistically save money, the plane must be reasonably efficient in both fuel spent and playtime spent. if the mission with the plane takes 20 minutes longer than with a rocket, it's hard to justify using the plane even if the plane costs close to 0 funds - simply because a disposable rocket would get the job done for maybe 10 or 20k currency and you can make a whole lot more than that in the 20 minutes you saved by doing some other trivial contract. a reasonably fast plane with a pair of aerospikes and a pair of ramjets can hit orbit witin 5 minutes or so. landing takes a lot more time and effort than the reentry of a dumb capsule at 4x time warp of course, but if the design is somewhat stable aerodynamically and you figured out where you have to retroburn and what trajectory to aim for, you can also get a spaceplane down to the spacecenter within a few minutes. of course none of that matters if you have more fun using planes or if planes are one of the goals / constraints you set for yourself in that specific campaign. having fun trumps pragmatic effiiciency considerations. it's a game after all.

if the plane is desgined to fly to LKO with a few hundred m/s left i don't think it makes any sense to use nukes. i'd cut the nukes altogether and use 1 aerospike instead. saves about 5 tons of engine mass (which you could simply replace with 5 tons more fuel) and gives you 50% more thrust when the jets flame out (nuke has 60 kN per engine, a single aerospike has 180). when doing spaceplanes with decent amount of thrust, the most simple approach is to just aim for something like 10-15° climb and let them run hands off. no need for fancy ascent profiles - those are only really relevant for very tightly optimized configuations that have to go supersonic in level flight because they lack the thrust to accelerate beyond transsonic while climbing. you have 2 ramjets on a tiny plane, so you can just find a suitable climbing angle you don't have to change at all.

i don't think you have to make the fairing that wide. the solar panels stick out a bit and the scanner antenna is a bit larger than the 1.25m cross section, but the conical shape is impractical. try something like this maybe: https://imgur.com/a/wgQynBy pointy at the top, no sharp edges, mostly cylindrical body. as long as you don't oversteer and keep it pointing prograde you won't even need fins

you could also redesign the lander a bit so it doesn't require a 4+ meter wide fairing to contain it. you probably don't need 2 terrier engines for a minmus lander of that size. a few small radial engines would be enough, really. if the fairing isn't much wider than the 2.5m profile of the launcher rocket, some of your aerodynamic issues will already be resolved by that alone. also i think you use too many stages and too many engines and not enough fuel tanks for an efficient launcher. a skipper engine with only the mid sized (3200) fuel tank is wasteful. skippers have enough thrust to push a 6400 (jumbo) 2.5 meter tank and payload. or you use a mainsail and 2-3 jumbo tanks and a couple of kickback boosters. the 1.8m booster rockets from the first image are way to powerful. i always found it hard to aerodynamically balance unrealistic rockets. once you change it to something that resembles a real world launcher system, it will probably work just fine. i mean there's a reason why real rockets look like they look :)

an alternative to reusing stuff is to simply design reasonably efficient rockets. even in the "hard" difficulty you still get 60% of the base income. for most of the contracts the advance payment alone is still enough to fund the whole mission even at 60% and the actual payment is still pure profit. if you tweak the income down even further (custom difficulty) you will have to reuse stuff to make a profit, but at that level the game can become a grind.

you can use this online calculator to do the maths for a so called "resonant orbit": https://meyerweb.com/eric/ksp/resonant-orbits/ if you want multiple satellites on the same orbit separated by specific phase angle you'd launch them as one vessel into a resonant orbit and then detach and circularize the individual sats at the PE. simply put you basically launch them into a polar orbit of (for example) roughly 50km PE and 200km AP and then circularize the first satellite on the first pass through the PE (ie. retro burn to get its AP down to 50km) and then circulatize the 2nd satellite on the 2nd pass. the other satellite should be (close to) the opposite side at this point in time. you can launch the whole thing in one go, even combined with the tourist bus vessel that goes into an equatorial orbit. you just do the munar transit burn with the combined vessel and then decouple the satellite carrier vehicle with the 2 sats and use a tiny correction burn while you're still near kerbin to change the equatorial flyby into a polar flyby for the satellites.

my usual "algorithm" to solve that problem is to break the required maneuvers down into 2 steps. step 1: put a maneuver node on your current orbit that lies on the intersection between target orbit and current orbit. easiest way to do that is to rotate the camera to the point where you see the target orbit "from the side" and to line up the AN and DN markers. if you click on the spot between the 2, the program will place a maneuver node that is on the desired intersection line (or close enough). then set a simple prograde maneuver that raises the AP of your current orbit to the target orbit. ie. at the end of the burn the AP will be at the same spot as the AN or DN marker of the target orbit (or within reasonable tolerance). execute the maneuver. step 2: put a maneuver node at the new AP we established with the previous burn. at this point you can tweak the prograde, (anti-)normal and (anti-) radial vectors to line up the projected new orbit with the target orbit in a single burn. i'm sure there are more fuel / energy efficient ways of doing it. but it works for me. makes satellite contracts pretty trivial.

if you didn't unlock the ability to EVA yet (i think it requires some building upgrades in career?) you can use the "Experiment Storage Unit" part. it has a function to collect all data from all experiments on the vessel. IIRC the storage unit part is unlocked by the same tech that unlocks the science jr. part it's a 0.625m part so you can (for example) put it between the mk1 capsule and the parachute or put it in a 1.25m service bay below the capsule.

don't worry about your piloting skills. we've all been there :) it's easy to overdo it. you don't need much input to get a stable rocket to orbit. you just give it a gentle nudge eastwards shortly after liftoff so it falls into a gravity turn that pretty much gets it into a prograde equatorial orbit with almost no further input (other than cutting the engines when projected AP reaches orbital height and performing a circularization burn once you get close to that AP) if it's a stable desgin with fins you can usually even turn off the SAS and it will keep its prograde orientation without any input and "fall" into a gravity turn on its own. or you set it so hold prograde.

looks like a decent tutorial to me. you should be able to replicate the steps in it. i guess the thing to take away from that video is that it makes sense to use more fuel tanks on your rockets. the vessel in the video has a similar engine configuration as the rocket you posted, but it has roughly twice as many fuel tanks for each stage. which means it will have less drag issues from accelerating too fast and the center of mass will move further upwards as the lower stages burn their fuel and lose mass, making it less likely to (try to) flip over.

if there is a kerbal in a command pod you should actually be able to use staging commands regardless of whether the vessel is out of power. being out of power only disables the vessel if it doesn't have a crew (or if the crew is sitting in a passenger module with no command controls) you'll still need electric charge to power the reaction wheels and line up the vessel for the next burn, though. so being able to stage won't really help if you don't have solar panels. or if the panels are facing in bad directions and will never be exposed to the sun. as a rule of thumb - either add a bunch of small panels in different directions (for example in 4 or 6 way symmetry) so your vessel can create some juice regardless of which direction it faces - or make sure that you only go into timewarp after rotating the vessel so at least 1 of the panels will be exposed to sunlight when the vessel is on the day side of the planet. also check if you're in time warp. i think staging is automatically locked while the game runs at more than 1x speed.

in my experience the aerodynamic properties of the capsule become less relevant if it sits on top of a larger rocket. i successfully used a 2 seat "pea" capsule mounted on top of some mid-sized 1.875m stack for the first mun landing in that new career for example. and that thing even had a bunch of 1.25m droptanks near the top, so it actually was a lot more draggy then anything a sane rocket scientist would build. fairings are also an option to make whatever capsule or payload you hide below them aerodynamic. regarding the ant engines and the gap in your rocket: you can use an "engine plate" part. applications like what you did with those ant engines are basically the purpose of the engine plate parts. the plate has an attachment node at the bottom, so you can add the rest of the rocket below it and it automatically adds a fairing to close the open gap in between. don't remember if the game actually has a 1.25m engine plate though.

the spherical (soviet style) capsules are pretty bad in my experience. i've tried using them in my latest career game and had issues getting them to orbit. try replacing the capsule with a cone shaped one (the basic "Mk1" Mercury capsule for example). also, the gap between the capsule and the fuel tank is bad. causes a lot of drag. you could probably just put that reaction wheel below the nosecone to avoid the gap. or put it into a 1.25m service bay. i can't identify the other gap between the upper and lower fuel tank, but whatever it is - you should probably avoid it.

after watching it again, i think it could be related to the fairing. it looks like the escape capsule falls out at the bottom of the upper stage thing and the fairing on the upper part is still intact. i suppose when you actually launch the rocket to space you deploy the fairing at some point? so maybe the chute in the escape scenario refuses to open because some glitch in the game logic makes it "think" that it's still inside the fairing. if that's the case you might be able to fix it if you pop the fairing open before you drop the escape pod out.

game shows the error message that the parachute cannot deploy while stowed. the video is kinda hard to follow but i don't actually see a parachute on the capsule. at least not where the leader line of the chute control panel points. so it's probably a clipping issue.

check the fineprint of the contract. if it's about a "new" lab, then refitting a lab that was already in orbit before you accepted the contract wouldn't count anyway - regardless of whether you use mods or some klaw - based contraption.

the mass of the upper stage should actually keep the CoM high enough i think. if i had to take a guess - the lower middle stage is probably too short. the reliant engine is kinda overpowered for the little mass it has to lift and the whole thing would likely perfom better with twice the fuel tanks (for both the bottom reliant stage and the upper swivel(?) stage). that makes it longer and keeps the CoM higher since the somewhat heavy (and unspent) upper stage will be further up. and you could probably ditch the two side boosters altogether if you simply double the fuel tanks of the central rocket (just a guess - but should be easy enough to verify with the Kerbal Engineer addin you use). EDIT: wait - judging from the ISP, it looks like those boosters are swivels and the upper stage uses a reliant. that's like the opposite of what they are meant for. the swivel has lower thrust and bad sea level ISP, the reliant has better thrust and decent ASL performance but is worse at higher altitudes/vacuum. anyway - the original point still stands - probably too much thrust and not enough fuel.

there is also a "fly by wire" part. it looks like a pointy 0.625 nosecone with an antenna in front. that component basically gives full pilot skills (stability assist, hold pro-/retrograde, hold anti-/normal, hold radial in/out, hold target) to the kerbal or probe core controlling the vessel regardless of their class/experience level. it's a little later in the tech tree than the baseline OKTO probecore, but much earlier than the high end probecores that also have the full suite of auto target commands.

the SOI concept is just a way to model different frames of reference in the unity engine. i doubt the engine requires an actual object in the center of the SOI for it to work. wouldn't have to be a black holy in any case. an abstract "center of mass" object would serve the same purpose (if an object is even required). i think in old versions of KSP the sun was only a bright spot in the sky and not an actual object and it worked. also, our sun is like 25,000 lightyears away from the center of the galaxy, so even if the game again shrinks distances to ~1/10th, kerbol would orbit the galactic center in throusands of lightyears distance and the next stars would be 1-2 lightyears from kerbol. so in normal gameplay it's 3 orders of magnitude further than the interstellar distances you're supposed to be able to traverse. i.e. in practice it doesn't *really* matter what's in the center. i'm sure someone would try (and succeed) to fly to the center just to see what happens, so it would be a perfect spot for an easter egg. home of the kraken maybe :)

i guess if ksp 2 uses the same "sphere of influence" mechanic as ksp 1, then the different star systems might simply be embedded inside another larger "galaxy" SOI to have a common frame of reference while travelling through the void. so once you leave the kerbol SOI, you're out in the galaxy SOI until you enter the SOI of one of the other stars. basically the same concept like when you leave the kerbin SOI and enter the sun SOI until you reach the duna, jool, eve etc. SOI - but one "level" higher that wouldn't be too far fetched imo. afaik our real solar system orbits the galactic core with an orbital period of 200 million years or so. i guess the same is true for all other stars in the galaxy. since each star has its own orbit, the relative positions / constellations of the stars change over time, but i guess the process is slow enough to be mostly negligible if the sci fi tech used for the interstellar travel in KSP allows travel times measured in years or decades.