I just found that the cabin fan doesn't work well from today. There is no air coming out unless I set the fan to maximal. Once the fan is set to maximal, there is strong air coming out, as usual, but as soon as it is turned lower a little bit, no air at all.

This happens no matter when I turn on the air conditioner or not. When AC is on and fan set to maximal, there is not much cool air either. Are these two problems related?

 

With those symptoms I would say that your blower motor resistor has gone bad.