Yes that is black mold, it's a problem in a lot of unventilated houses here but I've never seen it this bad. Shocking that somebody sleeps in that room, in other pictures you can see discarded inhalers on the floor.
The responsibility should obviously be on the landlord if it’s rented, but if you’re actually having to live there regardless then I don’t know why you wouldn’t attempt to clean it…
It’s going to come back again, but it would be better than nothing.