I've never had someone ask for my logs. Not an instructor, not a boat operator, nobody. I kept them in a paper book for the first 25 or so. Then I switched to using subsurface.
The only continuing education classes I've undertaken have been nitrox (no dive prerequisite) naui aow (25 dive prerequisite) and nase cave. I don't recall if there was a dive number pre-requisite but I talked to the instructor many times prior to undertaking the class and we probably covered it but I just forgot. I did switch to sidemount for cave and he wanted me to have at least 25 dives in the sidemount rig before we started.
The only continuing education classes I've undertaken have been nitrox (no dive prerequisite) naui aow (25 dive prerequisite) and nase cave. I don't recall if there was a dive number pre-requisite but I talked to the instructor many times prior to undertaking the class and we probably covered it but I just forgot. I did switch to sidemount for cave and he wanted me to have at least 25 dives in the sidemount rig before we started.