(I hope this makes sense.) Many friends have sent me dance requests, but when I click on it, it always shows the same user. None of the dances show other friends. I'm afraid to accept any of these dances now, because I don't want all the trinkets going to one user, when it was actually other users that sent the request.

Anyone else having this problem?

It doesn't matter which dance acceptance you click on. They ALL, and always have, point to the oldest dance. So if friend A sent you 10 dances all at once late last night, and other friends sent you dances this morning then, Friend A's dances will keep showing up until you've accepted all of those. Then your other friends' dances will start to show up.