Can the AC cause only a #3 cylinder misfire ?.......................No.

 

The way the computer calculates which cylinder is very complicated; including knock sensors that are microphones. Theoretically, banging on the block with a hammer can cause a P03xx. Along with "stuttering" sensed by O2 sensors, crankshaft sensor, MAP/MAF etc.

 

Is the AC compressor noisy if you have the hood open? Something still doesn't make sense. You didn't answer about the wiring for the coil and the injector on cylinder 3. No chew marks, or scraped wires?

 

Let’s give time to respond.

 

The idle speed drops just a little when the AC is on. When I installed the TTR engine mount, I got some vibration when the AC is on. Not nearly as much as you are getting, but noticeable.

The computer is supposed to compensate for the drag from the compressor. Now, if your compressor is on the way out, it's going to cause so much drag, that the computer cannot compensate. Your idle speed will drop down too much, and the engine will run very rough.

It's hard to imagine that it would cause a misfire in just one cylinder, false or real. It seems the one thing that you haven't done yet is remove the fuel rail and clean it out.

But if the compressor goes, you could get collateral damage in the rest of the AC system.

 

Pretty easy to check the AC clutch with your eyes. Check the AC compressor with a stethoscope ($5 at Harbor Freight)

 

not that I can see and I swapped the wires for the injectors with my other hhr but that didn’t do anything. Figured it was worth a try.
and I don’t really notice anything any noisier than normal. However I did notice a weird sound that seemed to be coming from around the front driver side wheel well area that sounded kinda similar to water draining out of a dishwasher is the best way I can describe it. And it was when that noise was present that the jumping was at its worst. It also occasionally will slam into gear at times. It’s not a constant thing but it comes n goes like a cycle after it’s been jumping bad for a while then it stops and the jumping seems to calm for a while as well. Idk this thing has been confusing me with all the different things it does then stops doing then comes back. Driving me nuts.

 

And I’ve been pricing compressors but it that something I can change on my own or does it require special equipment?

 

You'll have to take it to a shop. The refrigerant needs to be evacuated, then the compressor changed out, then the system can be recharged.