Phase Correct PWM library?

What do I need to change to use this Code (PWM Phase correct) on at ATiny85? Are the registers the same?

No, they won't be.

So if I would only count up to 50 (having a DutyCycle resolution of 2%) it would run at 160kHz (at 16MHz main clock)?

That sounds right.

 1 / (62.5e-9 * 50) / 2  = 160000 Hz

Is it right, that the ATiny85 can run with more... up to 64MHz?

I believe it can run faster, I haven't played with the PLL clock much on that chip.