1. Minimum connecting time is 30 minutes, so you should be fine, they are very good at transfers in MUC.

2. The baggage will be through checked if you fly on the same ticket all the way from the US to Athens.
The only thing you will have to do is to pass passport control to enter the Schengen zone in Munich.
It is exactly the same terminal building, the upper floor is used as non-Schengen zone and the lower floor used as Schengen zone.
So you just pass passport control, go downstairs, and then head for your next departure gate.

3. If the flight is late they have an excellent transfer service in MUC for passengers with very tight connection (because of late incoming flights for example).
They will meet you with a minivan at the gate and help you clear immigration and get to the next gate within a few minutes.
Otherwise if you want to take a later plane, Munich is a very nice airport to spend some time in.
The walking distances in MUC can be very long though (even though they have moving walkways).