The ceiling is definitely water leakage from above and the source of the leak needs to be fixed.

If you have a fire extinguisher, a periodic inspection should check for of at least the following items:o Located in designated place.o No obstruction to access or visibility.o Operating instructions on nameplate legible and facing outward.o Safety seals and tamper indicators not broken or missing.o Fullness determined by weighing or "hefting".o Examine for obvious physical damage, corrosion, leakage, or clogged nozzle.o Pressure gage reading or indicator in the operable range or position. 7.

The new IECC actually requires them, but most municipalities don't enforce the requirement (same as duct leakage and blower door tests). 

There are 6 units, and this is the only unit with the ceiling leakage in the bathroom

(See RCW 59.18.060 (13)) That documentation gives guidance that:Mold is caused by moistureMoisture caused by leakage problems are the landlord's responsibilityMoisture caused by condensation is the tenant's responsibilitySee also:http://www.doh.wa.gov/YouandYourFamily/HealthyHome...http://www.nwcleanair.org/pdf/aqPrograms/indoorAir...

Leakage in a line or a connection is one thing.

With water it can be 100 different things.If you can demonstrate the leaks to the water department they will usually do a bill correction adjustment for most of the leakage. 

Too many complications can arise (insect damage, rot, leakage, shifting off footing, and ultimately collapse if not consistently monitored and inspected) DO NOT buy the house without getting a proper inspection done on it first.

First vent to the outside for the fan and make sure there is insulation in the attic above this room and no air leakage into the room.

There may be a leakage so the stains.