If you are in a remotely suburban area, a 10' tall post near the compost pile will act as a raptor perch and take care of most of your issues.

Alternately, a "hot" compost setup generally is not amiable to rodents or other mammals.

I used a traditional bin[1], drilled some holes in the bottom and buried it 12 inches into the ground.

Prior to that we had a bin with a door at the bottom but the rodents always gnawed away at the door and got in.

[1] https://www.tensens.com.au/productimages/SAB78025.jpg

You can't stop the rodents.

Bury the nitrogen rich stuff in carbon rich stuff, like fall leaves.

Cats.