I finally figured out the last three pics. That is dirt on silicone sealer around a shower enclosure. Yes the dirt will often grow mould (mold) and the solution is to remove the old silicone sealer and replace it. Clean the bathroom and you won't get the black dirt. It is normal for any older bathroom, especially one that is rented. Why, because renters tend to neglect the place, expecting the landlord to maintain everything. Yet they also tend to complain if the landlord wants to come in. So you get this type of thing - dirt. We see similar moldy dirt in the window channels. People that clean up their living spaces and wipe the dirt off once in a while don't get this kind of dirt. The stain around the sprinkler head could be moisture from a leak or condensation on the cold pipe. Those other stains, who knows? Replace the ceiling tiles if it is a concern. If you are reacting to those typical, minor stains, you will not find safe rental housing anywhere on the planet, IMO.