How prevalent are abusive advisors?

From PhDs: the tortuous truth:

Overall, 21% of respondents said they had personally experienced harassment or discrimination, and the same proportion reported experiencing bullying. One-quarter of respondents who identified as female reported personally experiencing harassment or discrimination compared with 16% of those identifying as men. The highest rates of harassment or discrimination (24%) were reported in North America, and the lowest (18%) came from Australasia.

...

In the survey, 57% of students who said they had experienced bullying reported feeling unable to discuss their situation without fear of personal repercussions.

From A message for mentors from dissatisfied graduate students:

In the survey, 21% of respondents reported experiencing discrimination or harassment. The same percentage also reported bullying. Of those, nearly half said that their supervisor was the perpetrator

It looks like, by the numbers, 1 in 10 PhD students will be harassed or abused in some way by their supervisor. Anecdotally I think that abusive advisors burn through students at a higher rate that normal advisors, so I'd actually guess about 5% of PhD advisors are a serious problem.

I will note that your experience will vary wildly based on gender and race. You are much more likely to find that inappropriate or abusive behavior from faculty as a woman, for example. It's hard to generalize because an advisor who is perfect for male students may be abusive to female or non-binary students.

That said, the abusive part of academia is smaller than the part that isn't abusive, but will apologize for it and gaslight victims into silence. That's the fraction I'd be more interested in quantifying.

It's an interesting research question and difficult to answer since many cases are unreported or without details. I agree with the comment by @benxyzzy.

As far as I know, bullying in academia is on the rise. The short answer is: basically there are no specific data records of this kind of abuse and qualitatively speaking this is as prevalent in academia to a level that any PhD student should be self-aware and warned beforehand about the issue. Because this affects human health and academia's reputation. There are prescribed mechanisms in place to avoid this abuse but they are not practical. Most times the practical solution is to split up the supervision, which goes unreported and does not help the institution. The Nature survey gives good insights. Other data sources:

• I found this dissertation commenting that there is a vast body of empirical research on incivility in higher education.
• Some student ombudsmen make annual reports like this one from the University of Oslo.
• Tara Brabazon talks about bullying, gaslighting and toxic workplaces, commenting that there is plenty of research about that.
• Some journals on higher education may have empirical data-based articles like these ones: PhD student-supervisor relationship-Is there a problem?, Hierarchical microaggressions in higher education.
• Regarding your second point, there are plenty of articles on authorship issues like "coercive authorship" "honorary authorship".