Just reporting back on my own question:

1. Getting back to main building was a bit tricky. Staff at premium terminal was happy to help, but would not let me take the bus back because it was "to late" (1 hour ahead of printed boarding time = when the bus gates will open)
The reason was that getting back to main building includes passing through security once again, and 1 hour was deemed not to be ample time.

In fact, the easiest way is to "refuse" to board the premium bus when deplaning and take the economy transfer instead. (try not to show the purple BP, as staff will try to help you go to "the right" terminal, as you obviously don't know your own best I did this my second time to DOH, and it was no big deal (just be prepared for long queues to security scan)

2. A C-class passenger (without silver/gold status) cannot enter Oryx lounge free of charge, but may enter the business lounge (close to gate 11)
But here you cannot buy entry for a friend, so the solution is either to pay for both at Oryx lounge or to stay apart. (And if you choose to stay apart, the person with c-ticket may as well stay at premium terminal)


And added knowledge:
Staff you encounter at economy terminal will tell you you are in the wrong terminal (in a friendly way of course). So, for example, if you want to enter the business lounge in econ terminal, you may need to "persuade" them you really want to stay here.