If you don't have the CT researched, and invade a planet with CT buildings, do they work or do they go to "NONE" until you research it?

They work. You can even extract them and use them on whatever you want.

thanks ^^. If selling planets with CT stuff on them, does that factor into the price usually?

Yes it does in fact it's usually a pretty big factor.

CT buildings are considered artifact buildings
all artifact buildings work regardless, even if you are not in rank range to get it(mission not unlocked or NPC not etc)

the "not work" thing only applies to researched buildings.
I'm not entirely sure if it applies to blueprint buildings thou

It applies to blueprint buildings. If you don't have the blueprint, it doesn't work.

Yes it applies to bueprint buildings as well, I recently invaded a planet with a sulcation portal and an exotic lab and both had NONE on them.