Q1: Don't stay at the airport. Especially if you are going to stay near the Hauptbahnhof. It is only a ~15 minute ride to downtown. Go downtown, see if you can check in at your hotel, and then go from there (maybe take a shower if you can get in the hotel, or just wander around downtown if you cannot). You will be happier than staying at the airport. You can buy day tickets for the transit system, so you can always ride back out to the airport easily enough to meet your brother later on.
Q3: I agree with etch5895, do not spend that much time in Frankfurt and spend more time in Munich or elsewhere. We once spent ~24 hours in Frankfurt at the start of a trip and then 2 days in Munich on the way back. 24 hours was rushed, but enough. My suggestion with your Saturday arrival and since most museums are closed on Monday, that you leave Frankfurt on Monday. (I would possibly say Sunday night, but you are coming a long way and will probably still be jetlagged, so it might be useful to spend 2 nights in the same place at the beginning.)
BillJ