[cannonfoddertfc]

I've read a lot about the 34 carb and the 009 distributor combination, and I took pictures of mine to ask you all if you can tell me which carb and distributor I have. If I have the 34 carb and 009 distributor, what are my steps to get it running right?

Those pictures show a 34pict3 and a 009 distributor.
Here is the thing though, the worst symptom of that combo is a flat spot (hesitation) when accelerating. And it can usually be jetted out.
I know the horror stories but have seen hundreds of engines running this combo and they all ran just fine.

As for your issues, tell me a story about all those burnt wires. You have numerous wires with melted shielding. Hot oil does not do that, that is usually evidence of shorted electrical.

 

[cannonfoddertfc]

By jetting out, I was referring to larger jets but I dont think that is your problem.
They may be gunked up, especially if the cars sits without running for extended periods of time.
Ethanol in the fuel is horrible, especially long term. Probably needs cleaned but again, I dont think the carb is your problem.

It is not running properly on all 4 cylinders. It almost acts like the timing is 180 degrees out or two cylinders aren't firing.
Really hard to tell from the video. This one is going to require more diagnosis than I can give to you over the internet.
Recommend you find someone that knows aircooled vw engines.

And better have someone chase your wiring harness for a grounded lead.
I would look at the reverse light lead coming off the coil first.
Again, you will want someone that knows aircooled vw's. The circuits aren't the same as a ford/chevy or anything else for that matter.

BTW, full oil capacity is less than 3 quarts on that engine. Check the dipstick with a cold engine.
Anything more than that and it will puke out that breather filter you have there.