Give 'em a few more days. Mostly, what the check is about is to see that your character conforms to the rules as pertaining to game mechanics (ability scores within range, right number of skill points, feat prequisites met, that sort of thing). Unless you sent your background along in your email, don't expect any mention of that.
Again, no reason your character can't hang out at the Red Dragon while you're waiting for approval.
Again, no reason your character can't hang out at the Red Dragon while you're waiting for approval.