Re: air pump function
I'd bet $50 that the relay armature has stuck, closing the contacts and making the pump run all the time.
The only other thing would be a shorted transistor on the PTCM pulling the relay in, but that would be a very rare occurrence. (And a more expensive fix.)
If the relay is bad, SOMEWHERE on here someone (180?) found a cheap, aftermarket replacement. The relays just solder in - no need to buy a new board!