Non-CRTC PETs (Original PET, early 30xx) are fixed to 60 Hz.
CRTC (6545) based PETs (40xx/80xx/8x96/9000 - *1) use screen refresh rates set by its ROM (*2). 50 Hz for European machines, 60 Hz for US/Canadian units.
Regarding the details:
For the European models there was no need for compatibility with European television standards as far as I'm aware;
You're right. As self contained system, there is no need to synchronize to any external source. Why Commodore switched to 50 Hz seams strange. There is no technical need nor any legal to do so.
did they also use 60 Hz refresh? Were there any situations in which a PET monitor did not use 60 Hz refresh?
Early did. Later not. The majority of European units did use 50 Hz.
was the same true of the CBM-II hi-profile models with their built-in monitors
Basically yes (as well as for external screens). So 'regular' 600/700 units for Sweden and Germany (distinction due keyboard) were using a 50 Hz refresh. Except 'regular' is a wide array here, as there is a wide variety of ROMs for the CBM-II series, all of them at best beta versions. So yes, they did use 50 Hz, but which did or did not is hard to tell.
*1 - As a generalization this means all BASIC 4.0 machines.
*2 - The ROMs differ as well within the editor ROM for keyboard layout.