Reactordrone

Make sure you're in target mode on the navball, point at the retrograde marker and kill your relative velocity. Turn around and point at the ship at the pink "target prograde" marker and thrust gently towards it. That should bring the prograde marker close to the centre and you can then use lateral RCS to line it up to dead centre and keep it there as you close on the target.

If you have a controllable target vehicle you can switch to it and point its docking port at your incoming ship, then switch back and point your ship at the docking port on the target. It saves having to move around to align with the port.

Here's an early two stage design with thrust limited hammers. It is over the 18t limit of the un-upgraded launchpad though (solid boosters are heavy).

This is where you're going to run into problems. Most of the time people will raise apoapsis to the level that they want and then shut down the engine, coast up to that point and relight the engine to raise the periapsis. To get a circular orbit without doing that you'll need to maintain a very low thrust level and time it so that you approach your apoapsis just as you're reaching orbital velocity. From your description what you appear to be doing is trying to raise your periapsis beyond your current altitude while still within the atmosphere but all you're doing is raising your apoapsis and getting a highly elliptical sub-orbital path.

For other planets I'd probably do a Hohmann transfer just before, or just after the optimum to arrive just outside the planet's sphere of influence and then circularize to match the planet's orbit around the Sun. For planets with more eccentric orbits like Moho you might want to time it so that you arrive near apoapsis of periapsis to avoid large radial burns.

That should have enough delta-v to get into orbit. I recreated it without the real chute parts, ditched one of the monoprop tanks and got a 30t test mass into orbit with no control issues going up or coming down. I'm assuming the fuel in the reusable section was meant for consumption by the Rhino rather than as payload. I'm not sure this will be economically worthwhile since you're ditching the most expensive parts to return empty fuel tanks and cargo bays. ETA- Thrust to weight ratio on the pad is reasonably high so you can do a fairly aggressive push over (10°) just off the launch pad which might help.

I suspect the thrust from the separatrons is hitting the wing and applying a force to them. You should still be able to use separatrons but they'll have to be angled to prevent the exhaust from impinging on the shuttle structure.

With the stop/start method used in the tutorial you should be in target mode throughout the final phases of the docking, burning retrograde in target mode to kill your relative velocity to the target and then boosting towards the target. You should only be burning orbital prograde and retrograde to set up the initial rendezvous.

A gravity turn (or an approximation of one) is the usual method of getting into orbit and getting into orbit is the usual first step to going anywhere. Orbiting is all about going horizontally at high speed and the gravity turn gives a good, gradual change from going up (to get out of the thicker parts of the atmosphere) to going horizontally and when done well it doesn't require any control inputs after the initial push over. To know how far your fuel will get you you'll need to know the delta-v of the ship and the required delta-v of the trip. There are plenty of delta-v maps out there that will give you an idea of how much delta-v you'll have to pack and for working out what your ship's delta-v is you'll need the Tsiolkovsky rocket equation, there are mods out there that will calculate it for you or you can do it yourself fairly easily. The other option, of course, is trial and error and the sandbox is a good place to test designs and you can pretty much get anywhere in KSP by just playing and learning from failure (or successes )

I agree. In order to shoot straight up to the Mun you need a higher thrust to weight ratio in your upper stages and that leads to extra weight and lower delta-v. As an extreme example I made a small probe for a recent challenge which is quite capable of landing on the Mun or Minmus by getting into orbit first but if you launch it straight upwards it will run out of fuel at about 300km altitude.

You could try selecting and de-selecting the CoM indicator.

It does take a long time with the small unit though since you only get a 10% return on the ore input, i.e put in 400kg of ore and get out 40kg of fuel so you need to mine a huge quantity of ore to refuel.

I'd also suggest using a different site for picture hosting since that one seems to be riddled with malware.

Possibly mod related. https://www.dropbox.com/s/5l5itb8iqs26om1/Screenshot 2016-07-29 19.43.34.png

Not quite sure what you mean. Is this during launch? How are you trying to "align" the apoapsis? Pictures might help.

I generally face the probe normal or anti-normal. They should stay in that orientation and have their side mounted panels facing the sun throughout their orbit. I'm pretty sure spinning won't help in the stock game since it gets cancelled when you timewarp or when the ship is placed on rails when you return KSC.

Are you in an area with zero ore concentration?

The Dynawing is unstable if you use all of the fuel (the centre of gravity moves behind the centre of lift) so you might need some low speed flight testing of the shuttle section and a few aerodynamic tweaks. I did a couple of test flights and had an unrecoverable flat spin on the first one (the crew compartments survived impact) and a very low altitude recovery the second time with a successful landing. Both re-entries went into severe spins in the mid atmosphere so I think the problem is largely the design rather than the piloting.

Staging is disabled until the tutorial is completed but you can manually decouple the transfer stage and activate the lander stage's engine by clicking on them to bring up their menus (no idea how that works on console). Having said that, the transfer stage should have plenty of fuel for the transfer and circularization burn so you may not be getting the most efficient encounters and may need to change where you're placing the manoeuvre node to get the Mun intercept. You want your apoapsis to be similar to the Mun's orbital altitude and just over 45° ahead of the Mun in its orbit.

For landing, place a docking port on the top of the rover/lander and click control from here. That will re orient your navball for the landing. The other option is landing on your tail and tilting forwards, with thrusters to slow you just before you hit.

With the control modifications the ship is orbit capable so if you do the polar orbit with the periapsis just inside the 70km mark as Zophos suggested you should be able to hit all of the contract points with very little battery use. Once in orbit the reliant's alternator will have charged up your batteries and when you power down the stability control your battery won't drain. That should leave you enough power to manoeuvre for orbital boosts and the de-orbit burn.

Accept all rescue contracts, try not to kill or strand anyone and give them reasonable living space on long missions.

If the fins add control and stability that wasn't previously there then the funds aren't wasted Struts are the EAS-4 strut connector. If you haven't unlocked them yet it doesn't matter but they're something to keep in mind for later builds. Only 1 set of radial decouplers can attach to a booster due to the tree structure construction in KSP so there's not much point adding a second set.

Easy fix. Move the steerable fins as low down on the core as you can and add another four low down on the boosters. You had too much drag up near the top of the ship and very little natural stability so it tends to want to turn backwards. The lower the fins are the more the vehicle will want to turn into the airflow giving a natural, hands off stability to prograde. Edited to add- I also don't see any struts for the boosters. It's not much of a problem on this design but as the booster get bigger they can wobble on the radial decouplers and cause the engine thrust to vector around in an uncontrolled manner.

If you're not in control of the ship (or have another ship within physics range of it) it will happily orbit on rails without any drag effects when it dips down to 54km so it is possible to abuse that little game quirk to get a rescue ship to dock with it at apoapsis and boost up to a stable orbit.