Timer on Attiny85

I suggest leaving millis on timer 1 and using timer 0 for your experiments.

I certanly will

You should first initialize all the relevant registers to 0

I see the point, and I will do that too, although I don't see that often in the tutorials.

Thank you for your help, it is not easy for me to understand the attiny datasheet, at least not at the stage I'm on now.