Loose AFN: Troubleshooting & Fixes

Hello, I'm having a problem with my Audi A4 B5 (model year 1996, engine code AFN) since yesterday. I hope someone can help me.
Yesterday evening, after driving 200 kilometers on the highway, I arrived home. I was slowly driving down my street, looking for a parking spot, and I turned into a driveway. When I put the car in reverse, I noticed that it started vibrating intensely and swaying back and forth, almost violently. I then cautiously drove forward, and the same thing happened. So, I opened the hood, and I saw that the engine was swinging back and forth as if it wasn't even bolted down.
'However, the engine speed appears constant to me, and it seems to be responding normally to the accelerator.'
I stopped the car for now and spent this morning looking into it further. It starts normally, but the exhaust fumes are quite unusual, in my opinion. The more gas I give it, the worse it gets! It might be due to the engine tuning; I hadn't really noticed it before.

Does anyone have any guesses? Is it likely to be a mechanical issue, or could there be something wrong with the engine block itself, causing it to run on only 2-3 cylinders?
Please give me some advice. The car has 167,000 kilometers on it.

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More likely a mechanical failure, or could it be something within the engine block that's causing it to only run on 2-3 cylinders?

You should first test it to see if it runs on all cylinders. Let it idle, then disable each cylinder individually by disconnecting the corresponding fuel injector. If the drop in RPM when disconnecting a cylinder is, for example, zero, then that cylinder is not firing.

What are the fluid levels like, and what color is the smoke?

The smoke appears to be a whitish-blue color, I would say.
Could it be the head gasket? But if that's the case, wouldn't the engine not run at all?
Are you saying that to fix the issue, you simply need to disconnect the fuel line at each injector? Also, the coolant looks normal, and I haven't checked the oil.

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Are you suggesting simply disconnecting the injector line at the respective injector during the process?

Sure, but put a cloth over it, because it's going to make a bit of a mess.

I doubt it's the ZKD (thermostat housing) in this case, because otherwise it would likely have pushed the coolant out.