In July my children father replaced the battery in my jeep, since our daughter was driving it he felt he needed to. After the battery was replaced when you shut the jeep off about 1 - 2 minutes it would start making sounds from the dash board, then after you got back into the car there would be a terrible smell. I was told the sounds was the vaccum hoses. Then recently if I turned on my a/c a light smoke would come out of the vents and no air blowing tried the heater the same thing. Then yesterday the car completely stopped, after I looked under the hood, I couldn’t believe the size of the battery it was so small, after several calls to the father to find out where he purchased the battery I went to the place, they replaced the battery free of charge. May question is could that have messed up my a/c - heater system sinc eit was replaced in March 2008 by the dealer when I purchased it.
No I don’t think having a too small battery could have damaged your A/C. If you had the problems when the car was running, your alternator would have still been providing sufficient voltage and current. I don’t know what those “terrible sounds” from your dashboard were or the smell, but I don’t think it could have been from an incorrectly sized battery, providing it was installed properly. Perhaps you have multiple problems.
It is possible that a “right” battery for your car may be smaller than the original battery. Of course it could have been the wrong battery, but nothing you noted would point towards a battery problem.
I would want someone to check out that car and find out where that smell is coming from. Give them the whole story.