Is it acceptable to ask to videotape, or do most girls not allow that? Has anyone ever done it?

I haven't but know people that have.  It's a personal preference thing with the lady, and I wouldn't suggest it on the first meeting.  She needs to feel comfortable that you won't publish it anywhere she doesn't want it to be.  And no, I never saw that one (not that I didn't ask, lol)

But I certainly would not advise it until you get to know her. Even then, I do think a majority of providers would not really like the idea, but some will really get into that.