hmm ,lets have a look...
1) If you destroy the hanger of a space station, will it not produce any more units? I have seen space stations without hangers build units.
In multiplayer I have taken out a hangar but then it seems to repair itself. I cant remember how this happened. I think its when the Station upgraded.
2) Do imperial ships that carry ties produce forever or do they only carry a certain amount?
They carry a limited amount, which is about to be reduced in the next patch
3) Can you repair your ships?
Nope. If you have one battle, and lets say you won but have a lot of damaged ships, if you fell under attack again, the next turn, those ships will automatically be fully repaired.
4) Do damaged space stations level down in galactic conquest?
erm? what do you mean here.
PS: welcome to the forums!