What can I do with broken (burnt) rooms?
If you leave a machine without maintenance or endure heavy earthquakes, it's likely going to explode at some point, leaving you with a burnt room that you can't sell or rebuild.
Is there something to do with it, some way to pay to repair/rebuild it?
Nothing. The room is never going to be usable again, and the space in which the room was placed will be permanently unusable.