When I send a recommendation request, does each REU request a different "style" of rec letter? I want to apply to quite a few REUs and I'm asking a professor to write me recommendations. I was wondering whether for most REUs, he could write one recommendation and then use it for everything, or whether he would have to rewrite or edit the letter for each program. This is so that I don't feel bad "spamming" him with requests from various programs.

Also is it a faux pas to put down the professor's email into the request box in the app without sending them an email? (Even though I discussed this briefly some time ago with professor)
Before you put their name down, email the professor again just to make sure they're still ok to write the letter.

Once they've agreed, don't worry about the different formats that may be required for different places. Professors are generally fully aware of what the letter writing process demands and would not (or at least, should not) commit to it unless they know they have time for it.

In your initial email, it may be a good idea to list the places you're applying to and their respective deadlines, so the professor has a rough idea of the time commitment.