That motor looks pretty rough,probably not turning very fast.
I'd buy a cheap $20 50cfm exhaust fan at nearest box store.
Pull the motor and mounting plate out and install it back in yours,should go right in there with no changes.
It will gain a little efficiency with combustion air brought in from outside,but will work either way as long as it has enough combustion air.
What is his reason for issues with 2nd pipe?
I'd screw it on to an outside faucet and open the valve to see what you have for pressure.
Anything much over 70psi will cause problems with pop off valves on water heaters,and fluid masters on toilets.
Do you have the model number off of outside unit so we can make sure of size coil you need?
Biggest thing is to get a coil sized for the tonnage of outside unit,and to match the width of existing coil so it will fit existing plenum.
Make sure your new coil is a 410a coil so you can reuse it if...