If an email message sent to one's professor is not answered promptly, is it rude to forward it without comment to the original recipient as a reminder? If so, how long should one wait before doing so? Assume the professor is teaching a class the sender is taking.
On the whole, I'd say "yes, this is a rude way to send a reminder to a non-peer."
The premises are tricky: what is "prompt" to one person is not to another, and not everyone checks (work-related) email at every available opportunity. E.g., some seem to only go through email once a day, on weekdays, or even less often.
There is the other issue about acknowledgement of receipt, even if one's response will be delayed.
But/and if one is teaching a course with 30 or 100 or 250 students, individual responses to daily can be a time-consuming occupation... so that "acknowledgement of receipt" becomes unappealing and an arguable waste of time... if a proper understanding can be reached.
I've tried to cultivate in my students a sense that emails should have a "greeting", a "body", and a "closing", much as old-timey paper letters did... if only so that one can tell whether a thing was mis-sent and/or truncated, not to mention some overt acknowledgement of the identity and dignity of the recipient.
So, if I were to receive a fowarded copy of an email that had already been sent to me, I would consider it quite rude, yes. I do attempt to respond within a few hours of receipt of all email, even if only to acknowledge receipt. Whether or not I had done so, I'd view a merely-forwarded email as uncivil, apart from issues about peer-or-not.
I would be at a minimum annoyed and further less receptive in such a situation where someone would send a plain forward of an already sent email.
On the other hand, when I need to take such action, I do not send a plain forward but instead I assume the recipient took knowledge of the original email, and add some recent relevant developments (eg: since our last exchange, two new students joined our team efforts and work is really being done. Regarding the original email, everything still stand, please give us an update whenever you can...) or something to that effect