Gaarst

Use Pythagoras.
You have a triangle CSR (Kerbin Centre, Satellite and Receiver) which has a right angle at R (because tangent).
So: CS^2 = RS^2 + CR^2. SC (distance of sat to Kerbin centre) is x + 600, SR (distance of sat to receiver) is 2500 and RC (distance of receiver to Kerbin centre) is 600.
(x + 600)^2 = 2500^2 + 600^2. In the end the altitude x of the sat is 1970 km.

No, as far as I know not in the stock game; even if they are placed in symmetry, the Thrust Limiter bar only affects the engine you have selected. There are however some mods that can help you handle your engines, for example the two below (I don't use them myself so I don't know if they do exactly what you are asking for, but it should be good enough either way).
 

"Required but not produced" means you have means to store electric charge (batteries) but not to produce it: solar panels and RTGs produce electricity (so do some engines with their alternator, but I'm not sure if the game counts it in the engineer report thingy), batteries store it.
With just batteries you will be fine for a while but you will eventually run out of electric charge, making your spacecraft unusable.
If you are doing a short LKO mission it shouldn't be a problem, but for longer missions you will have to watch your batteries carefully. Also note that transmitting science back to Kerbin consumes a significant amount of electricity.

Part Angle Display is what you are looking for; it has been unofficially recompiled for 1.3.1 by linuxgurugamer (see the last post in the thread).
 

The Mun, Ike and all of Jool's moons are tidally locked. Gilly and Minmus aren't. A tidally locked moon rotates around itself in the same time it rotates around its planet, this means that it is always showing the same face to its planet. The Moon IRL is tidally locked to the Earth: we only see one side.
While a moon may be tidally locked to its planet, it doesn't mean that it doesn't have a night and day cycle. The "dark side of the Moon" is not always dark, it has a day/night cycle as long as its rotation period (which is the same as its orbital period since it's tidally locked): the "dark" side of the Moon is fully lighted by the Sun during new moons.
It's the same for all the moons in KSP: they have a day/night cycle where each day lasts one rotation period, whether or not they are tidally locked. When standing on a tidally locked moon, the planet it is orbiting will appear not to move at all even if days and nights happen (it would move north and south in the sky if the moon has a non-zero inclination, like Bop and Pol).
For a body to not have any day/night cycle it would need to have a rotation period equal to its orbital period around the Sun, which isn't the case for any planets in KSP.

Not possible in stock, but there's a mod for that (not updated for 1.3 yet).
 

Yes, launch to the West. 180° is an equatorial orbit, only opposite the usual way. Remember to pack a little bit more dV since you won't be using Kerbin's rotational velocity, but rather be fighting against it.

The reaction wheel is probably too powerful. Reaction wheels and control surfaces do not respond to input the same way: reaction wheels pretty much apply full torque instantly while control surfaces take some time to deploy and react depending on the airflow. By forcing your craft to move using the reaction wheel, you "throw" your surfaces out of the airflow by the difference in response or simply because the torque of the wheel exceeds the torque the surfaces can apply/withstand.
Reaction wheels and control surfaces usually don't work that well together, but it can be amplified depending on the craft itself (ie: shape, CoM and CoL positions...).
It's just an hypothesis but SAS is known to destabilise crafts when too much torque is available. Kind of hard to say for sure without a picture of the craft or a craft file.

Space coordinates are defined according to the celestial sphere, ie: they don't change as the planet rotates around its axis or the Sun. A LAN of 36.4° on Y1D1 00:00:00 will be the same as a LAN of 36.4° on Y80D129 01:07:44, or any other random date you can come up with.
This means that you need to launch at the right moment to get in the right orbit, since it won't "drift into position" as Kerbin rotates. The easiest (and most efficient) way to do it is to launch when the target orbit is right over the KSC.

If TAC LS works the same way with RO as it does without it, you'll just dump the excess WasteWater/Waste/CO2 out of the ship once you've filled it.
W/WW/CO2 tanks are only useful if you want to use recyclers, or if you really care about realism and don't want to magically get rid of some mass.

I did.
 

Most mods are already in their dedicated folder inside GameData, so you don't need to do that. Otherwise it doesn't prevent any mods from working AFAIK.

Wheels physics are still a bit wonky, even after the numerous patches of 1.1 and 1.2. While it has gotten better overall, some weird things still happen, especially with the non-steerable fixed gear (you're "lowriding" as soon as you touch the runway).
To help with this, you can try messing with the spring and damper settings (as you already did) which my help, or you can try to land more gently which again may or not help.
There are probably some fixed made by the community, but I can't remember any off the top of my head (I know @GoSlash27 was pretty involved in this in 1.1, so he might be able to help you better than I did).

Drag and lift are functions of density (and speed squared).

Are you using Windoze 10? If yes, then the problem might come from Windows. I had the same problem; killing the Desktop Window Manager through the Task Manager restarted it and fixed the problem for me.

Press F2.

There is a bug report here.
The issue seems to be linked with the highlighting FX, deactivating it in the options should remove the stutter. Squad should be aware of that and a fix should be in 1.2.1. (Info coming from the bug report itself)

I believe I've already seen that issue here in the forums.
To get the best chances to see this bug fixed, you'll have to fill in a bug report at the Squad Bugtracker describing the issue. Reporting bugs on the forums is useful for people to see it and discuss them, but as the console versions are very new and no one (talking about the community, not the devs) really knows how to fix their bugs, submitting an official report on the bugtracker is the best thing to do.

Engine alternator. For some reason, they act as batteries, but with less than 1 unit.
If I had to guess I'd say that engines can't spawn EC out of nowhere so it is added to a small battery inside the engine and then redistributed to other batteries/pods across the craft.
Probably a consequence of some wierd engine module since solar panels don't have this.

Depends on the design, some rockets are extremely stiff while others behave like noodles.
Screenshots would be helpful for a precise solutions but here are a few things you can do to reduce wobbling:
Add struts Reduce gimbal on your engines Disable SAS (beware you'll have to stabilise the rocket yourself) Disable reactions wheels: less control, but also less wobble Avoid having reaction wheels far away from the CoM (command pods on the top of the rocket are a good example of this) Control the rocket from a part closer to the CoM of the rocket: the CoM doesn't wobble a lot and SAS is applied at the controlling part (not CoM), so SAS will not overcompensate for the wobbling, which would cause even more wobbling. Make the rocket shorter/thicker: tall and thin rocket are more wobbly Try to avoid linking putting light/small parts between heavier ones: the joints are usually weaker and the rocket will wobble more (especially the large reaction wheel between two tanks) Reduce the number of parts as much as you can. Not always possible, but often the simplest and best solution. If you're that desperate, install Kerbal Joint Reinforcement

F4 disables vessel indicators in "staging" view. Chances are you pressed it while quicksaving (F5).
I think it resets when you restart the game, if the game is still running, simply press F4 to get the indicators/distances back.

Some (most) mods work with only one version of KSP. Typically, a lot of mods for 1.0.4 were broken with 1.0.5: you need to update the mods as well, you can't just copy the folders of the outdated mods.
The best thing to do is a completely clean reinstall, then reinstall the correct version of each of your mods and place the backup of your saves in your new folder.