I'm wondering if a new 13 SEER air handler a) wouldn't fit in the wall compartment because of the size of the larger coils.

A lot depends on the final output: is the coil blocked with debris (even though the unit is overcharged with freon)?

Another thing I did was have my A/C coils cleaned and repaired along with a leak being fixed for $300.

This is very easy to do if you have a brad nailer with 2" brads.

Account ClosedElectric baseboard heat works the same manner as the electric resistance heat coils in the electric forced air furnaces with which you are acquainted.  

I had a buddy of mine who does mold inspection look at the video and he says its more than likely just dust build up and the coils just need a good cleaning which is a couple hundred vs the $1050.

A typical service on AC units is cleaning the coils, throwing the High/Low gauges on it to check pressure/compressor performance, and putting a multimeter on the capacitor. 

ALL the tell tale signs had been replaced; ground wires, refrigerator coils, and plumbing connections.

* Freezer - Let's say you have a freezer which has been scraped and has punctured coils

If there was a pet in the home, those refrigerator coils are magnets for pet hair.