"Rats carry many diseases such as salmonellosis and leptospirosis that can be transferred to your chickens. They can also carry mites and fleas into the coop, which can then infest your entire flock."
It wouldn't hurt to do a deep clean. It is much better to be safe than sorry. Rats are gross...
Definitely not a cat. A cat would have chosen your chickens over eggs. A raccoon would have eaten the eggs and probably went for the chickens. The poop does appear to be a rat's poop. Maybe the rats were trying to get nesting material and the eggs got in the way so they kicked them out.