GFs will get the same kill bonus that your characters get, so if you want to level them up faster, use them.

Omega is always level 100.

I think it's too late for the card sidequest, if you havent' done it, then you can't do it. If it was any other disk than 4, he'd be in the lobby of balamb garden waiting for you to play enough cards that he will challenge you. If you had done the quest, he would be on the ragnarok, but I don't think the CC members show up on the ragnarok if you don't do the card quest.

You can do an angelo search (turtapods and t-rexaurs are probably the easiest enemies to do this on) and hope invincibility items come up eventually.