What are the rules for cooking in a non-kosher kitchen with kosher utensils (pots, cutlery, etc).
- Can a microwave be used if its contents are double-wrapped?
- Can the burners on a non-kosher oven be used?
- Can dishes be washed in a non-kosher sink?
Partial answer from summarizing this OU article:
In both a conventional and microwave oven, double covering the food in foil or plastic is sufficient. (The article explains what the concern is.) A covered hard plastic container is, itself already one layer, so all you need is to cover that in a layer of plastic wrap or foil. An aluminum pan covered with a sheet of foil is all one layer. Then cover that in another layer of foil.
Regarding the stove burners, I am citing an excerpt from another Mi Yodeya answer
After the Return by Rabbis Mordechai Becher and Moshe Newman, a guidebook for baalei t'shuva, covers this
You can cook on a non-kosher stove so long as the burner ring is clean (he doesn't cite a source).