Pollen filter wouldn’t be the problem if there was still air coming out, I’d guess.
Depends. On mine the fan is on the car side of the pollen filter. If the filter gets really plugged up the fan will pull car air past the not-very-sealed seals on the car side of the filter, essentially recirculating car air.
Coolant issue? Leak or not circulating through the heater core (have you tried getting the car stupid hot so that even if it isnt dry air it is hot air, which will hold more moisture?)
Since you say the rearview mirror is fogging, not just the windows, I’d be checking for puddles, or stuck on recirc, or filter is wet or puddles in the air intake system (leaves in the intakes at base of windshield, e.g.). The windows will fog partly because the rain cools them off. That shouldn’t happen to the mirror, it should be warm therefore the relative humidity is too high.