Of course you shouldn't think about your portfolio at all during work. I think that's not professional.
Why not? Just because you're thinking something while at work then it isn't professional. As long as it doesn't affect the work load then it's fine
That depends on your job
For example, if you are a neurosurgeon, then thinking about your cryptocurrency portfolio while performing a brain surgery may not be the best idea after all (even if it seemingly doesn't affect your "workload"). Regarding questions raised by OP, I think the best approach is to change his timeframes, i.e. to switch to longer-term trading. In this case, checking the market once or twice a day will suffice (say, in the morning and before bed, though before bed can give one a sleepless night)