1) No idea. I think the planet can fall but I read on the forum that the defection rate is also dependent on the morale score of your target. Others say that trading with your target also helps a great deal to flip the planet. Remember that some races are loyal by nature and are harder to convert (although a 40-1 ratio is pretty stiff). Perhaps there's a Secret Police Centre or whatever it is called that prevents a planet to be conquered culturally.

2) Influence Starbases only affect influence within their sphere. Any starbase creates its own influence. An influence starbase takes the influence within its range and amplifies that. It doesn't affect anything outside its range.

3) I don't think foreign relations affect your influence effects but influence sure affects your foreign relations. If your influence starts to threaten your neighbour's planets, they will not be happy with you. When trying to fight influence wars, I've always ended up in real wars the moment the computer lost one or two colonies. It won't just wait and see, it will hit back because it sees you as a threat. As a result, I am seldomly able to fight influence wars by themselves, they're just preludes to real wars. Also, influence starbases are considered similar to military starbases so planting them near other people's planets is a good way to tick someone off.

1) Can a major power lose their only remaining planet to rebellion, or must it be invaded? I have had a 40-1 ratio in IPs on a last remaining planet for over 20 turns, and no revolt yet.

Yes, I have conquered many races and assimilated all their Planets.

2) Do Influence starbases add to the civ's overall influence total? Meaning is it worth keeping them around after you have conquered an area via influence, or better to just decommission them and take the few buck

Well they don't add to influence but they do counter any influence making them tougher to flip to someone else.

3) Are influence and foreign relations related at all? For example, is it easier to influence a friend, foe, or doesn't matter. Also, do relations suffer once a power loses a colony to you.

Nope you can take any planet but if you are taking planets and have a weak military you can be pretty sure they will attack you. If you have a big enough military they will threaten you but not take action since they can't win. Your relations with them will just determine how many planets you can flip before they get angry enough to attack you.