2001 Dodge Neon - 172,512

ERROR CODES: P0301, P0420

Issues:

VERY rough idle
-Goes away when I turn the wheel, or shift to neutral.
-Not sure what method to try fixing this, drilling the throttle plate, computer reflash, motor mounts?
-Occasionally triggers oil light (3 times I think?) at lights

Occasionally "stutters" when I accelerate out of a complete stop
-Usually at stop lights, but occasionally stop signs, doesn't happen any other time.
-Spark plugs and wires were changed less then 3000 miles ago. Found oil in cylinder 3 recently but error code said misfire on 1?

AC Isn't Cold
-Heat works wonderfully, AC doesn't even get cold
-Proper refrigerant levels
-Compressor does NOT turn on - All fuses good (Unsure how to check voltage)

**Could this be the Relay or Low/High pressure switches? If so what do those look like and where can I find them to check voltage? **

http://imgur.com/RndrDqv
Plug that was dangling and I plugged into compressor (Found out this was very important)

http://imgur.com/1tTDRWb
Unknown plug - Help me identify!

http://imgur.com/2qToxmb
Plugs location - Passenger side, below lights


UPDATE: Mystery plug is what used to connect to the auxiliary fan (I THINK), I have an aftermarket radiator with a SINGLE fan and now that plug is useless, could this be the culprit of all my issues?

Any help, suggestions, and guidance is welcome.