Lets suppose I am idolized by the Legion. This means that Boone will not want to be my companion. If I suddenly decide to kill every legionary I see and become vilified by them, will Boone want to become my companion again? (I am just wanting to confirm this before doing it)

Im not entirely sure, but i dont see why not. But i would save do that and check, and if not just reload.

If Boone was your companion and he already voluntarily left you (giving you some speech) because you started to befriend the Legion/kill NCR (or whatever), you can't get him back. He's gone for good.

If he was never your companion and/or you fired him before doing anything that would PO him off....not sure. It's likely he'd join you, but if you did enough anti-NCR actions (killing certain NPC's, say), he may not. It's not just Legion rep but NCR rep that Boone keeps track of. Like said...save game and just try it.