Disconnected Loud (IMO Useless) bathroom exhaust fan
The accumulated dust is going to have minimal affect its performance as a fan. But feel free to vacuum/brush it if that makes you happier. Lacking a description of the noise, it probably needs bearing lubrication.

In many apartments, the bathroom exhaust fan is most of the ventilation you get. Not running it may lead to mold problems due to excess moisture build-up. Aside from being unsightly, mold can be bad for you.

The "big, hole-less square light cover" almost certainly has a gap around the edge to permit airflow.