2001 Beetle, smoke, rough

We have had a few problems with our Beetle recently. Water pump replaced a few weeks ago after coolant light kept coming on. Unfortunately the car was still run a bit with that problem, but with the new water pump seemed to be all OK.

Now the exhaust is a bit smoky, strong smell of hydrogen sulphide, and running rough at idle, with soot out of the exhaust. Sound like a bigger problem, and maybe linked to the overheating earlier.

Any help appreciated.

Can you test the coolant temp sensor as if this is out the car can run rich. Is there any chance that the timing belt was put back on one notch out? Also check all those vacuum lines as its easy to dislodge or split one....a lot of things get dislodged when playing with engines hey.
Good Luck.