[villagetinker]

The "other day" when you first noticed the MW not working and the breaker tripped, was there a storm in the area? This looks like this could be the result of a nearby lightning strike. If not, then the other possibility would be a loose connection in the plug/socket connection. This damage could be overheating due to a loose connection. The heat from the loose connection could easily cause the plug or cord to the MW to fail, and cause a short circuit causing the breaker to trip. If this is the case, replacing the receptacle will only fix half of the problem, as the cord set is probably damaged, and is now probably a fire hazard. I would suggest replacing the MW.

I looked at the photos again, and I see burn marks INSIDE the box next to the receptacle, this looks suspicious to me. Was anything else tripped at this time?

Look very closely at the receptacle when you replace it for burn marks, especially outside the receptacle. If you find these or anything that indicates arcing, please have a licensed electrician check the entire wiring system for possible damage.

Please proceed very carefully here, and I will strongly suggest you get expert help from a licensed electrical contractor. You do have a problem that if not fixed correctly may cause a future fire.
Hope this helps.