You said if you don't level up you can't get past the bosses. Excalibur II proves that this isn't true yes.

No all but one of the sidequests are cut off once you get to dics four of FF8. The tiem change that happens cuts you off form all the citys and areas you coudl go to to do all the sidequests. The CC Quest in justa minigame that does not really need to be played.
Dude cover spoilers. (SPOILER)Okay so what side quests are cut off? I get them all early but I don't see any reason for Odin, Research Facility or Mr. Monkey to be cancelled.

Must if not all sidesquests here can still be done swoedfighting is not ever a sidequest. But it is a minigame that gets you gil if done right.
Which sidequests? Chocobo, yes. Mognet, maybe but I don't think so.