Will current ceiling junction box support fan? Not exactly sure if a fan was mounted to it prior as I recently moved into this apartment. Somewhat older of an apartment and box doesn’t directly state if fan is supported or not. Figured it was better to check first.
Mount the fan to the joist or block behind the box, not the box
The two screws in the back of the box in line with the mounting tabs appear to land in a joist or cross-block in the ceiling. I would attach the fan to that using two 1/4" by 3" structural wood screws (not drywall, deck, or lag screws -- look for something with an ICC-ES or IAPMO rating, such as a FastenMaster TimberLok or Simpson Strong-Drive SDS) through the fan bracket and ceiling finish board into the structural member.
It may, but I concur with brhans. Drywall screws are very easy to snap right off and they (at a minimum) should be replaced by even just Deck Screws, which have the shear resistance of nails.
But, as with ANY apartment, call the Landlord and get their written approval and/or have them perform the installation and ALL electrical modifications...as is likely in your contract.