1. Will faction doctrine affect station tech level?
...
will differrent factions have custom stations?
You choose the tech level of the station (low tech, midline, high tech) when you build it, so it's not tied to doctrine. What blueprints you have available and prioritized will determine the station's weapons loadout.
Each station tech level has 3 tiers - "orbital station", "battlestation", and "star fortress". The tech levels/tiers will be distributed among the core colonies as appropriate. Given that weapon/fighter availability and ship quality are factors, I'd imagine that the same tech type station may feel a good bit different when used by another faction.
2.Will we see things like pathers stations with SO modules?
Given the above: probably not? I haven't looked at it yet, though. For example the pirate bases are all using the "orbital station" tier but with a range of missing modules depending on how powerful that particular base is. May do the same thing for pathers, may do something different; will see. SO is so heavily movement-oriented, though, and its penalty doesn't make sense for stations which don't have peak time, so probably not that specifically, if anything.
3.speaking of pathers, will they behave in a manner similar to pirates? They are basically just that.
I have some specific
plans. Let's leave it at that for now

4. How will factions react to you installing ai cores in colonies? I reckon it would *** off the Ludds and Hegemony?
Where would the fun of using absurdly powerful AI cores be if I told you what, if anything, may or may not happen as a result?
Will it ever be possible (or moddable) to directly control a station?
I imagine if you're in a situation where your colony is under attack, and you have only a small fleet/flagship but a powerful station, you might end up as nothing but a spectator. Controlling the station directly would put you center stage again.
Well, in that situation, you're not actually obligated to participate in battle and could let it resolve itself in the campaign layer.
More specifically about controlling a station, though - no, for several reasons.
First off, it doesn't fall neatly into the current ship-controlling UI setup. A station has multiple modules, right, and they're mostly cruiser-to-battleship-and-beyond level of power. There's no existing mechanism for switching between these quickly, having a good overview of the status, etc.
Secondly, I think it'd be pretty boring. You don't get to maneuver, and the primary driver of the flow of a vs-station fight - the station's rotation - is fixed and not controllable. The actual impact player control would make would be very limited compared to them controlling a ship. The stations are just not something that's well suited to player control, by design, since the goal of their design is to create a specific flow, different for each station tech level, that gives each fight character.
<stuff about pirates>
I hear what you're saying! I think I mostly covered it a few pages back, and you also touch on it in your post as well - the complexity here is significant, and there's just no way I could see putting in the time to both do it initially and then maintain/deal with design issues on an ongoing basis without having very clear and specific reasons for doing it in the first place.
"Could be interesting" just doesn't cut it given what's involved, you know? I could see extracting new factions out of pirates if that became necessary story-wise (i.e. Charterists in Askonia), but not just breaking them out into a bunch of factions wholesale. If - and it's still an if - a change needed to be made, my inclination would be to make it simpler, not more complex. Hence the thought about *potentially* fixing their player rep at -50.