I was wondering if it was possible to swap my Auto for an 02 CL-S's manual. Do you think it would fit?

yes.it wont be easy and your going to have to look into computer issues as well

What kind of computer problems? say i got to a shop that specializes in transmissions, would they take care of it?

Im betting the issues you would have could be fixed by putting in a manual transmission with its engine harness and manual computer.

a auto comp in a manual will throw all sorts of codes.
like...
converter lock up
internal slippage
possiable speed sender
vehicle abs codes. cuz it says its in park but your moving
etc...

not a big deal just make sure to get all the goodies from a doner vehicle.

shift linkage
pedal assembly
clutch master/slave and lines
ALL engine bay harness
ECM and transmission comp if it has one.
flywheel, clutch ,and all that stuff
better grab motor mounts aS WELL.