If you haven't swapped the TPS wires, that's definitely contributing to the issue. The throttle position sensor on the 2zz throttle body is on the other side from where it is on the 1zz, so at idle it reads WOT and at WOT it reads ~11% throttle. This causes all sorts of issues, but its super easy to swap.
The plug you're explaining is definitely the power steering pump switch. It is used to idle up the engine when the power steering pump is used. If you idle your car and move the steering wheel left and right, the engine rpm should dip a bit then rev back up. If it does anything else, plug that power steering plug in.
You should also definitely fill it up with all fluids before doing any more testing. When starting the engine for the first few times, it will definitely run a bit rough, but if you let it idle for a minute or two it should smooth out. Without a full exhaust on it, it will idle a bit high, but that's no big deal. With the coolant and other fluids topped up, its definitely ok to take it around the block to make sure everything's running right.
As for the OBD port, the Matrix wiring diagram shows a total of 6 wires going to it:
4 CG (Ground)
5 SG (Ground)
7 SIL (Straight to ECM, pin D18)
13 TC (Straight to ECM, pin D20)
15 WFSE (Straight to ECM, pin D19)
16 BAT (Fused 12v signal, 7.5A)
The Prizm/Corolla wiring diagram shows all but TC and WFSE, so just add those and you should be good. Attached is a diagram of the OBD port with the pins numbered. There's a flap type piece piece on the top and bottom that you have to unclick and fold back before you can add pins. I went to a junkyard and got a whole OBD port with wires attached to practice de-pining and re-pining, as well as to have a couple extra pins to add the TC and WFSE wires. Best of luck!