Not sure about managers, but (more) senior technical staff and team leaders are supposed to mentor the less experienced technical staff.

Whether or not it happens seems to depend on the team. Personally, I like teaching people new stuff so it would often fall to me, on the teams I worked in. ;)

Definitely. I'm a team lead (duties: mix of team management, project management, and some IC development), and my mentor is on the management team, and I mentor a junior dev. One of my prior mentors (as a junior dev back then) was the company founder/CEO twenty-five years senior to me.

Of course, that founder was one of the originators of XP practice, and ran our company on those principles--pairing, fast feedback loops, and mentorship for all (he's since handed over the company to his #2 who he mentored for a decade, and who is continuing those practices).

Definitely. I’m an engineering manager (admittedly at a startup) and I pair program with my team all of the time.