Leaving Munich for Rome on a Friday 8:45 am flight, how early do we need to be at the airport, should we stay at our Marienplatz hotel and take train or stay at hotel near airport?

Leaving Rome FCO on a Sunday 7 am flight, going to Vienna before back to US. Many horror stories on message boards about FCO, again is it better to stay in Rome or stay near (or at) the airport? How early should we get there?

If you want to stay at your Marienplatz hotel just figure in the 45 minutes it takes to get to the airport in Munich on the S-Bahn.

Since you are going to another EU country the security may be different but coming back across the pond you go through two security checks. Check with your airline for advice on how early they recommend.

You did not post which date you are going from Munich to Rome.
Normally it should not be a problem to stay at Marienplatz and take the commuter train (S1) to Munich-Airport. It goes straight, every 20 minutes (starting very early) and needs less than 40 minutes. If you start for instance at 5.21 or 5.41 am from Marienplatz station you can catch your flight easily.
There is one problem at the moment. Starting next Monday all trains will be on strike and the S-Bahn leaves every hour only.

Your airline's reservation should tell you the deadline.
MUC-FCO should be Lufthansa, departing from Terminal 2.
When you use self check-in for yourself and your luggage, you should be at the airport appr. 45min prior to departure.
But check your documents!

Thanks for the responses, trip is not until May, so hopefully strike will be over!