Tenant - no filter on return air duct, general mystery HVAC problems

Hi, I have been renting my first apartment for 9 months and management just came in today to change the air filters for the first time. The maintenance person discovered that there has been NO air filter in the main vent in the living room for the entire time we have been living here (and probably longer, since the last time maintenance came to change the filters).

The issues I’ve noticed:
-as soon as we turned on the AC for the summer, it broke. This happened in our unit and in at least one other, but not in the entire building. Management decided to replace the condenser, but we’re not sure yet if that has fixed the problem.
-the indoor air quality has been pretty bad, and all my roommates have had worse seasonal allergies than usual. Another tenant said the air from the vents consistently smells bad, especially when the heat was on in the winter.
-in multiple units, there are certain vents that don’t work and the rooms are not heated/cooled properly. The issue is worse for cooling, and air is not flowing properly through those vents.

My questions:

1. How big of a deal is the filter thing?
2. Does this sound like multiple different issues? From what I’m reading, it seems like unfiltered return vents could definitely break the AC.
3. Would any of these issues have been driving up our energy bills?
4. What maintenance do I need to request—air duct cleaning, coil cleaning, etc?

Thanks so much!