I've found a good resource here: Electronics - Henning Karlsen
If you open the PDF that corresponds to the Arduino Mega 2560 Rev3, you'll see the port labels there. For example PORTD 0-3 is mapped to digital pins 18-21. I hope that's right. I don't exactly know which revision of the Mega2560 I have, but hopefully the Rev3 mapping will apply to my device too.
The sad conclusion is that if people will try to use my code on other type of Arduinos (not Mega2560), they'll have to figure out where PORTD is mapped on their device.
So now what remains to be figured out is what is OE on the TPIC6B595 shift registers and how I can control it. Also, the questions a) and b) referring to CrossRoads' example code still puzzle me...