If a building is deemed not safe or fit for residency, and is condemned on that basis, the city can make you move out. They're revoked its occupancy certificate. The fact that the walls look okay from the outside does not mean that the wiring inside the walls is safe, or that there aren't other serious health or structural problems with a building. The owner's heirs are free to get estimates to perform repairs and to bring the building up to code.

Either the owner's wife had the legal right to burn the mattress or she didn't. The fact that she's charged suggests that she didn't. She should consult a criminal defense lawyer.