RE: the black smoke I just met with someone who had black smoke, bad idle, rattling noise, it was lifters worn all the way through the top and bad cam. A new timing belt shouldn't make this worse, it should just be the same. In his case, new cam+lifters/bearings fixed it.
1 and 2. No, the TB change should not cause this to the point where the engine is rattling as bad as you say. It could be a worn camshaft causing the dull thumping and pulsing, have you seen the videos in the camshaft replacement FAQ article? You should have noticed it before though.
3. Possible, everyone makes mistakes. I suggest putting the engine back to TDC, if the marks are all correct, it shouldn't be wrong. If you look at the picture of the camshaft hole on the head, it's possible to insert the pin if you were way off to the left or right. You said you checked it 3 times, is the tensioner arrow about where it should be? A little more or less will not affect timing.
The 2006 shouldn't be one of the rare cars that might have the round crank sprocket and use tool t10050. They should have the oval crank sprocket and use t10100. Some T10050 were defective from the factory and had the arrow in the wrong spot, the metalnerd tools shouldn't have this problem unless you somehow used the wrong arrow, even then it shouldn't change the position of the belt that much. Using the locating tools the cam-crank don't move.
4. No idea. The rag theory is a common mistake but you already said no. It's normally due to something simple.
6. A little brake clean should quickly evaporate. TDI can't take much fluid without hydrolock so if you really poured it in, enough to cause a small puddle, it's possible it wouldn't have burned off before bending a rod. This doesn't sound likely to me but it's a possibility.
Was the injector wiring harness adjusted? Maybe some wiring that rubbed through was touched and finally broke? This normally throws a code though.
Are the motor mount bolts all secure? You're supposed to use new bolts. If you reuse the old bolts or strip the aluminum mount the engine can shake.
Also, post moved to mk5 section since it's gone beyond an intro.