The only 2001 AWW Golf I had those issues with was hit by lightning and the ECM was bad. Before we go assuming the worst, run and save a complete Auto-Scan with the current VCDS-Lite release and post the results.
If possible, see if someone in your local area has a genuine VCDS system, like the KII-USB or HEX-USB+CAN, click Options -> Test and post those results with the communication outcome of the engine Key On and Running at idle.




