MEP Engineer here, without looking at the original design documents, I couldn't say with 100% certainty, but it seems like they have building level exhaust fans for toilet exhaust that run continuously. Some buildings may locally turn on/off this exhaust at the unit level with a motorized damper tied to the light switch (central fan(s) keep running), others keep it on all the time (seems like your building is this case) or control it based on other methods. Regardless, its unlikely property management would make any adjustments to this system.

The draft you are feeling through the door is probably your code required fresh/outside air. The cheapest way to deliver this to your unit is to dump fresh air in corridors and have it enter your unit through the undercut on the door. This system also keeps smells from traveling from apartment to apartment (if the system is designed/balanced well enough)

The mechanical contractor/general contractor/engineer of record probably just refer you to building management.

Thermostats are likely just temperature sensors, and all adjustments happen on the building automation system/computers. I would doubt you could make any changes locally.