AC unit (turned on year round) leaves so much ice in the blower causing no cooling (pic included)
I'll let someone else take a stab at helping you fix your immediate problems, but I'll take a crack at the deeper issue. From your profile, I see that you live in New York. Assuming your mother does as well, your climate is wet, but only very hot for a few months out of the year. Running a central A/C unit year-round simply to dry the air out is a gross misuse of the equipment, and is probably making the house freezing cold for no reason, at high cost, and putting unnecessary wear-and-tear on the poor thing.

If your mother needs dry air to alleviate her asthma, have you considered using a dehumidifier to dry the air? It'll be a lot more inexpensive and cost-effective than running the A/C all the time. That must be costing a fortune.