I know that the time greatly varies from professor to professor, but what are some good 25th percentile to 75th percentile estimates? And does the time spent reading/replying to emails generally increase when the professor is teaching a class?
What are some other factors that influence the number of emails a professor receives?
I'm not sure what the exact percentiles are, but I'd estimate that most faculty members who handle their own emails (more on this below) probably spend on the order of an hour a day or more dealing with emails.
I think that emails don't necessarily increase when one is teaching as opposed to other times of the year—unless there are no TA's for the course. In that case, since the professor is the only contact point, emails will rise, although this depends on the course enrollment.
Other determining factors are more or less obvious: the more active and senior a professor is, the more emails they will get:
Professors with larger research groups will have more email traffic associated with group management.
Professors in larger departments will have more email originating at the department and committee level.
As professors move up the ladder, they are asked to participate in more reviews and external programs, which increases the burden still further.
On the other hand, one advantage that many senior faculty have is that they may have dedicated administrative assistants, whose responsibilities can include filtering out the unimportant messages for them.