Let me take a crack at these:
From your first post:
1) It might be a precursor installation, they can spawn ruined cities, ground forces, ammo dumps etc, sometimes they're defended sometimes they aren't, or maybe it is an NPR but for whatever reason they're unable to make ships right now, maybe a mineral crash?
2) Sensors get severely myopic at tonnages below what they are set at, the sensor design screen gives you some idea of this where it tells you the range against 1kton, 500 ton, 250 ton, or 50 tons, you can see that you get something like a third the range against half the tonnage. In general it's a good idea to make small resolution sensors until you get large dedicated sensor ships designed for finding capital ships at extreme ranges.
Study this chart:
The elcheapo 60 hs sensor is close to the one you fielded, notice it has a max range of 60 million, but against a 750 ton FAC that range is reduced to a mere 3.5 million which is a 17th the range against a target a quarter the size , since your sensor is a higher resolution again I would estimate you would get maybe 70,000 km's range. Which isn't enough to even detect them before they can hit you, considering that the game runs in 5 second increments and the FAC's travel at 9000km/s they can travel 45,000 kms per increment and possibly you'll be within range of their beam weapons.
3) Black holes generate constant pull towards the center, 1,000 km/s per level. Ship speed is reduced by 1,000km/s per level so you can't have any stationary objects in a black hole system. I'm not sure what happens though if you try to park a ship with a high enough top speed at a waypoint.
4) Toughness of those FAC's will probably depend most on their speed and if they use any kind of point defence, if they're meson equipped and fast you might need to waste a lot of missiles to score a hit.
5) Civilians will not use jump engines, so as long as you don't add a gate that system is safe.
Your other post:
4) You might want to design some big passive sensors so you can spot carriers and other large capital ships from longer range without making your position obvious like active sensors do.
6) No idea about enemys in black holes.