Spricigo

I suppose it results in less overall fuel used (although not sure) also it's less fuel paid with Funds. However refuelling at Minmus allows for a smaller interplanetary ship what I feel it's the most advantageous result we can get. But, as always, it's a matter of choice and compromises.

The only possible way to win the rover game its by not playing it.

His tutorials are quite nice indeed. Something to consider when looking for KSP tutorials: the game changed a lot through the versions, something that used to work in early iteration may not work anymore so be cautious with old content. But there is some awesome stuff like this constant descent landing: No, its not easy like he make look to be.

which is not the most (fuel)efficient way, but since we are talking about Minmus(is near and has low gravity) that is hardly a serious concern. Later in the game 'proper' landing procedures may serve you better (inverse gravity turn, constant descent trajectory, suicide burn are some concepts to look for). Also you may adopt some mods to help you with this or any part of the game you find too difficult or simple uninteresting. Or simple enjoy doing it in 'unproper' 'inefficient' way because what really matter is only how much fun you have.

your method is the numerical analyses of the problem. It or algebra should lead to same conclusion, with imprecision depending on the approximations done. Drag is probably the most unpredictable factor by far. So probably the best to face with guesswork rather than with maths.

to add to this, About piloting: slight differences in the procedure can lead to a huge difference in result. A few seconds, a few degrees a few dozen kilograms. About contracts: try to learn, as quickly as you can, which contract are worth doing and which ones are a waste of your time. e.g testing a part at launchpad can be done in a few seconds without expending any Funds; testing part flying faster than 1000m/s below 5km will require serious consideration about thrust, control and heat. Both contract have similar rewards. Notice that there is more to consider than just "how much Funds the rocket will cost" vs "how much Funds the contract pay", there is the time investment, how likely are you to use the mission to do something else, how much you enjoy doing the mission.

why not V²=Vi²+2ad ∴ d= Vi²/2a Where a={(T/m)-g} (as a first approximation trajectory is exactly vertical and mass is constant) which may not be so bad for a booster landing back at Kerbin SpaceX style, but if we consider that mass decrease, the actual distance will be less than we calculated. We can still use the formula if we use the average acceleration (not so simple because variation is not linear). Adding other factors (drag, change of Isp, fuel consumption, attitude) can make the calculations pretty quickly. So I'd start with this and see how good it works out before considering such factor.

Maybe a more empirical approach works for you. Do a few attempt to execute the maneuver by yourself to get a idea of what commands are necessary and then try to write to replicate it with a script. Refine and iterate until you get a reliable and consistent result.

Notice that maths 5used in the mentioned thread can still be applied. But we need some adjustments, we need to disregard the burn to circularize at periapsis (we will not do it) and also consider that the orbital velocity will depend on orbital heigh and semimajor axis (refer to vis-a-vis equation). There is also the problems of timing and non-instantaneous change in velocity to consider. But seems that the Oberth effect is the principal difference.

If you need to keep throttle at 75% to avoid wobbling you should consider to reduce/change the engines to cut the extra, unused power. This will, in turn, reduce weight and may allow reduce fuel amount. Keep goling until there is nothing left to reduce

Nailing a smooth gravity turn is the number one design goal of any of my launch vehicles. But since I'm a mediocre pilot further limited by keyboard controls the number two goal it's to allow it to happen with minimal player imput. A much underpreciated skill mindeed. Maybe because a screwed gravity turn is much more noticeable. About the contract, any part of a craft in the requested situation will suffice. A small probe, launched on top of a hammer (trust limited) can do it quick and cheap. Something along these lines:https://kerbalx.com/Spricigo/SL51D Or in a truly kerbal way you can try to make a debris survive after crashing at Kerbin with the vessel you used. (supposing it cannot perform a proper landing)

Never seemed easier this way for me. But I started to decline this kind of contract very early. Adding to this, different contracts are solved easier with different approaches. For example: to test a part at high altitude/speed consider launch a powerful, even if not much precise, rocket. For doing science at a given location low powered and maneuverable plane works best. Also you may, and probably will, find some contracts not worth to do. Try to avoid those, you may wait the offer expire with no penalty or actively decline for a small penalty. (on normal game I do it for every contract is don't want without problem)

Just say what tech is missing and we can try to figure out the alternatives. While what @HvP said is solid advice and may help to solve your problem there one point that would be better if you don't need to adopt. That is: changing the Reliants for Swivels. Let me explain, yes it may help you to control the rocket. But is always better if you remove the problem instead of countering it. Gimbal in particular solve the problem by causing another, which is your thrust not steadily at direction you want but moving around to counter the wobbling. (to make things worse the cause of wobbling may be excessive gimbal) Well, we don't know what is the intended purpose of the ship, so we can't say if reducing some stage is possible. ( Or if spreading into lateral stack, for the matter.) But making the rocket shorter may also help. (on a side note, I'm curious about the destination)

Which is worse than we supposed (stable at normal flight unstable at reentry) Get rid of those empty tanks and fix the cause of instability. Since I can't see, I will try to guess, but you have 20t of engine in the rear and 1t of cockpit in the front? There is no way to have a good balance without adding a lot of deadweight. With the increased weight you need more wings for lift and control surfaces for control, but that add drag so you need more engines. And the cycle start over. Define a purpose, build the vessel and then remove. Remove weight, remove drag, remove power. And keep removing until you can't remove anymore. When you become proficient you'll not put so much unnecessary things to start with and find more to remove. Another point: looks like you decided big=cool. If that's your opinion no one can say it's wrong. But different approach can also be cool, look at something build by, for example, Wanderfound or AeroGav. Their vessels may not 'fit your style' but certainly there is lot to learn from how these guys design spaceplanes.

Well, for launching satellites you can't go much cheaper than 1st stage SRBs do most of work, 2nd stage finalize the orbit and optional 3rd stage for orbital maneuvers. (or some variation). At this conditions (SRBs are dirty ship, 2nd stage is just a small tank/engine, 3rd don't return) recovering its hardly worth the time. So I suggest to just go cheap and cheerful for small payloads. Another point to notice it's that you should not design recoverable vessels for the sake of recoverability. Instead decide what you want to do and design a vessel that do it better (cheaper, faster, smaller, cooler..you decide what 'better' is), that is the first and most important decision of a design. A design will be good or bad depending on how well it fulfil its purpose (e.g I have no use for https://kerbalx.com/Spricigo/Kaingang in my career game, its ugly, limited and not cost effective, a very successful design anyway, got me a badge, a few downloads and comments. {as a side note I need to update it sometime...but I need to do so many things}). Now about you more pressing problem, craft capable of ferrying kerbals to orbit and back: what is the techs available? what did you build so far?

Instead of building a shuttle that ascend like a rocket and descent like a barnyard door you did one that fly like a plane all the way. ...So AeroGav. I guess its hard to you endure a shuttle that have 'just enough' stability for controlled glide to runaway. But that is the idea behind the concept. Since the wings (in a typical shuttle) are not used during the ascent the concern with mass and drag asks for minimal amount. Likewise the main engines are not vacuum engines but atmospheric engines, preferable with large gimbals to deal with asymmetrical thrust, asymmetrical drag and shifting CoM. And since we are rocketing our way into space we want all engines lit at once right at the launchpad (except, maybe, for a much weaker and efficient orbital engine) Looking at your typical design I'll be much surprised when you show up with something like that.

I suspect FNORD FNORD FNORD

Which is the designed flight profile to the RL STS. Much better than spinning uncontrolled like the KSP STS replicas usually do. AeroGav, surprisingly enough the Swivel is a viable option for Shuttle lite. But if you are dealing with asymmetric thrust, asymmetric drag and shifting CoM then Thuds, with 8° gimbals, are serious contenders. All in all, shuttle (even the one in real world) are very kerbal design. There's so many reasons to not work properly but yet it get the job done.

There's several ways to build a shuttle notice KSP shuttles don't look like NASA shuttle. The reason is because something that looks like the real shuttle probably fly poorly if at all.

I'm guessing : blank space may be because some other celestial body get in the way? There is a lot of.... Transit (forgive me) around Jool

I'm afraid something during the updates (including mod updates) have damaged your save and it finally broke. It's not the first time I see someone reporting this problem, unfortunately didn't find the other thread but also a game initiated in older version (IIRC 1.0.5) and after some updates no ship was considered new. Can be 'solved' by alt-f12 contract into completion but that become bothersome pretty fast. I think a bug reports and wishing you luck is what can be done. Let's hope I'm wrong and something easy can solve it.

Maybe also relevant : this is a game initiated in a earlier version? How many updates it endured?

You can use Flyby finder to find slingshot opportunities both in the way or at joolian system. Alternatively you may try to ask nicely and hope someone can help you. (don't look at me, using trial and error myself)

Well, you noticed that mistake. Yet you did it anyway. The first improvement I propose it's to get rid of this unnecessary oxidizer. Something important, if we are to help you, is to know what the purpose of the plane is. Without knowing the purpose it's hard to give food advice. That said: Try to balance the craft so the CoM stay around the geometrical center. If possible CoM ahead of GC because it makes easier to design a aerodynamic stable plane (as in don't flip when slight off prograde). Place the fuel tanks and cargo bays in such way that the CoM don't shift to much (ideally not at all) when you burn fuel or delivery the cargo. Engines may be moved to shorter lateral stacks further ahead to help with CoM but it also may cause drag. You want to avoid drag as much as possible, unfortunately everything causes drag. Thus don't bring anything you don't need, if you bring don't expose to airflow if you don't need to, if you ou expose to airflow make it count. Do you really need the rearmost landing gears, the cockpit or all the intakes? The ship is built to allow minimal fuselage exposure to airflow (wing incidence) ? Do you 'closed' all nodes with matching nosecones or other pointed part? The control surfaces are limited(both in authority and surface area) to not change the direction more than necessary? (in this regard a SSTO spaceplane follow a pretty straight trajectory with very gentle changes of direction. Some behemoths can be kept under control with close to no control surfaces. Well, that's general advice. For more specifics I'm waiting for more images, maybe a craft file but, most of all, a defined purpose.

Important to notice that you "carry" the results of previous maneuvers. Let's say you planned: departure from Kerb, gravity assist at Eve, another gravity assist at Eve, gravity assist at Kerbin and finally arrival at Jool. But when you departed from Kerbin you weren't precise so, while you still meet Eve, not as close as you planned. You need a correction in the trajectory or you will miss the 2nd encounter with Eve. And by consequence, not reaching Jool on the planned date. Eventually a new encounter with Eve (or another place net) can put back on track. But that may be too late if some contract expires in the mean time.