Questions are fine. Be aware thought, that you can touch on things that noone actually knows (at least noone not developing the game).
Overmatch. Your 10 ship destroyer fleet attacks a 10 fleet destroyer fleet of equal strength. With a 1:1 ratio the destroyers pick one target each, engaging in 10 different one on one battles. With 5:1 five will attack one target, and the other five another target. If the 10 sit around a gas mine that is attacked by a single ship, it should also decide how many jumps in to take that ship. If one equal destroyer comes, it could be 1 or 5 depending on overmatch setting. I have not tested this a lot, though.
I prefer a higher overmatch factor to gang up on targets hard to kill them. Dead or fleeing ships don't damage my ships. Also, I suspect that with 1:1 you will struggle to kill anything, since normal designs flee at 20-50% shields. So in the 10 on 10 destroyer battle, the difference could be between winning and losing, and killing ships vs just forcing them to jump away.
As far as I know, you can't build another empire's territory. The exception is if you get mining rights and such, which typically is between friends. You can of course also take the colony giving the territory by invasion, or try to move the borders by establishing colonies just outside their zone of influence.
For the design and energy use.
First, try to read this post on energy balance for a ship:
Now, specifically for the space port, keep in mind the designs top right panel:
The top number is energy collection. To gain some, install energy collectors. Notice the static energy usage below, if collection is higher than that, the space port won't use fuel in everyday operation. Now, what else is there? For a space ship there is hyper space travel, movement... Space ports don't do that. But there are also weapons and shield recharge. If you want the space port to be able to fight without using fuel, you need to have enough energy to also fire the weapons and recharge its shields. A crude aim is to have the same energy as the reactor output, but designs could use a fair bit less energy than this in some cases. What you need to never need fuel is enough to cover static + weapons + shield recharge.