Q. Can one use (in prison) a microwave that all the non-Jews are using for their cooking and warming up?

The problem is that the staff just does not cater to just Orthodox Jewish people.
How do I kasher it? Can I kasher it?

A. Kashering a microwave oven is a complicated topic in Halacha in the best of settings; in your case (in prison) it is almost impossible. (See answer 319 in this forum, concerning koshering a dishwasher or plastics).

The simplest way to use this microwave is to wrap completely the food on paper napkins or towels, or place it in a closed paper bag.

Horav Shlomo Miller Shlit’a suggests to double wrap it if possible, if not one layer suffices. Liquids should be warmed in covered containers.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a