One further wrinkle about "home" systems. One of the now defunct early expansion mechanics was when a faction expanded into a system, it sucked a faction from the target system into the expansion source system. So it is possible now for a faction to be located in a single system that is not its natural home system. I understand that if it retreats it reappears in its original home system (in the same fashion as an expansion). I haven't witnesses this in the wild yet, but this is the way it should work.
Yes, I actually witnessed that.