The property management company should be repairing that stuff, especially the furnace. If it is the inducer motor, then one day it just isn't going to start. This would result in an emergency call and the problem will cost more to fix than if they were to repair it before it breaks. I would look over your lease very thoroughly. In my experience the resident cant do their own work on plumbing, electrical, HVAC etc. The issue is mainly an annoyance at this point and the furnace is working otherwise. So it may be tough to get those repairs covered. As far as uneven heating goes, adjust your vents. It's presumably a forced air system, so you just need to force that air to other parts of the home. Keep the vents closer to the furnace closed more than the ones in the rooms. I would start looking for another place to live. There are much better companies out there. This is just the beginning. How will they perform with bigger issues?

Source: been in property management for 20 years.