Spricigo

@AeroGavhad a rule of thumbs of one air-breather for 30 ton of craft. Given than people still refer to the plane/spaceplane tutorials  he wrote, I guess it may be a good starting point.
In any case, you will need to design>test>iterate as suggested by the previous answer.

That by default  is control trim. And may be the reason why your navball is wandering around.  Alt+X will reset trim.
Precision control is now a mode, Caplocks toggle it on/off.
 
Well, maybe  cheaper, cooler or something but strapping a parachute to recover the thing is as convenient as it get. 

One alternative is the  EVA resource transfer Mod.
PS: I'm afraid it may not interact well with the inventory system, tho

Well, if you can't figure out a use by yourself you probably don't need it. If that is the case, leaving it alone or terminating is as good as anything . If you keep it they may eventually unlock contract to expand the stations, if you terminate the game don't need to keep track of it.
Otherwise, the parts are functional, drill can get ore, labs can do research and so on.  If your mods allow that , the can also be rearranged or recycled.
 

I'm guessing there. But seem like how % of max stack (bar) and itens in the stack (number). Itens that don't have are unstackable.
 
 

a combination of clever tricks, post prodution and...wait for it...     Mods!!
 
 
 

They "just appear", not sure if sentinels find them too. They are a lot rarer than regular asteroid, so it may take a while. 
Maybe there is a config somewhere to make them appear more often but I'm not aware.

It seems that the craft is barely stable, at some point it just go past the limit and there is no coming back.
Maybe it is the CoM shifting back as ablator get consumed, maybe is some of those micro-wobbling going just a bit too far from progade.  In either case the solution is to move the heavy part further ahead and the draggy parts further behind, probably adding some heavy/draggy parts for this particular craft to work.
 

@antipro the, rather unappealing, answer is: not in stock KSP.
You probably need to take a look at the mod's thread to be sure it's not a mod version issue or a mod conflict. 
Also keep in mind that the SoI transitions skew the prediction quite a bit and Gilly SoI is not exactly a large target.  So, a more refined maneuver may be beyond what the mods can provide.
 

You are looking for [Post-burn Rel. Inclination]. AFAIK KER don't display it by default, you need to set it.

Higher TWR don't cause aerodynamic instabilities, it may cause overheating  and it certainly increase the drag losses (gravity losses on the other hand, will decrease. Net effect is "depends"). However this craft is not overheating and is quite capable of reaching the desired orbit, how adding fuel  will improve it? Exta fuel don't seem to be necessary or useful. Maybe you are trying to fix what is not broken (and only making the craft more expensive in the process). 
As for why the mod supposedly didn't work as advertised, @AHHans,  already nailed it: it works exactly how it is set to work. I'd try to increase the [Hold AP Time Start] to 80, if I understood the parameter correct, that will keep the upper stage pointed prograde while the time to Ap drops from 80s to 50s.
 
IMHO efficiency is an overused word by KSP players. *shrugs*

In that case the most useful tip probably is: don't rush it.
Notice you don't want only to get to the same position your target is, ou also  want to match velocities  when you get there. That is a lot easier if you take your time to do as many small adjustment as needed  to get closer and closer to it.
That was precise to the point.* The means already matching  the velocity direction. If you know your closest encounter lies several orbits ahead, you can reduce the magnitude diference with gradual adjustments every time you pass that point.
 
*...and to the pun. NO REGRETS!

That's not something we see very often. Try to dig kerbalx.com or the spacecraft exchange subforum. 

That's not something we see very often. Try to dig kerbalx.com or the spacecraft exchange subforum. 

You can set your antenna to [allow partial] and transmit. Will take longer since you will need to wait for recharging but will be done eventually.
Or you may send a supplementary power unit with an outlet to plug the lab in

deadlineType = None  

Since I become aware of independent throttle and Axis Groups, crafts I use don't have RCS anymore, just small retroengines if necessary. 
Gut feeling says 5-10 units/t (45-90m/s RCS Delta-V) is OK for most pilots. That assuming RCS thruster are balanced and reaction wheels take care of rotation. 
 
 
 
 

Keep in mind that there is a good reason for the unrealistic rotation/momentum in KSP. 

Don't quote me on that but I think it may be. Have you tried to leave it further away the runaway? 
 

Yep!
You will also need some practice to really get the hang of it. 

Not gonna work you will run out of EVA fuel before reaching a closed trajectory.
you could try to go to EVA and 'push' the command pod and before you run out of EVA fuel re-board and EVA again (with a replenished tank) and repeat. But that would be tedious and difficult.
 
well, if you zoom out in map mode you can see Jeb's orbit around the Sun. It's unlikely he will hit anything (space is mostly empty) and since there is no Life Support in the stock game he can stay indefinitely in orbit. And rescuing him later will be probably easier with things like solar panels and  more advanced probe cores, also with more player experience too.
 
Meanwhile a good idea is to try to figure out what you did wrong to end up in this and other bad situations, to avoid doing it again in the future. How about talking about  the rocket you launched, your goal  and how you were handling it?

In Stock, relay antennas have the ability to further extend your communication network and ask as a Node between the Control Point (KSC or Remote) and your active craft. In Remote tech all antennas have that ability.
Now if you want a antenna, in Remote Tech, that don't need to have a target to work what are you looking for is a Omnidirectional antennas. You find a list of the antennas in remote tech and their stats in this link. Notice that it don't even mention which ones are relay since that is not a thing in RT.

There are mods for that. One is Ship save splicer.
 

Seems you already solve the problem. But in a 'brute force' approach, so I suppose you may still be interested in what exactly happened and a reliable way to avoiding it infuture. SO:
CoM not in centerline (look at torque values given by KER)
Almost certainly the culprit is the payload, try to make it as symmetrical as possible. Don't be ashamed to use the offset tool. Also, if possible, use fairing to avoid asymmetric aeroforces.

How about cheating a replacement?