As other people said, you won't have to claim and re-check your baggage.
I would add that I had multiple times short-time layovers in Munich, even just 55 minutes and I never had any problems, even when my flight had a 20-mins delay.
Munich is a very large airport but signs are everywhere so you will know where to go and should be fine!
Your bags should be tagged for Copenhagen and not made available to you in Munich. As you will not have time to leave the airport during your layover, head straight to your connecting gate, without passing baggage claim. Your entire layover should be in terminal 2.
Arriving from an airport in a “safe” country you should normally not have to go through ...
You will NOT have to claim and re-check your bags if the entire booking is under the same ticket. When you go to drop off your luggage at the US airport just confirm with the agent that they'll be booked all the way through to your final destination.
As far as checkpoints, you will have to do both security check and passport control, from my experience ...