People are talking about invites and stuff for the dance and I do not know how to get them or what they are for. Can someone please explain?

in order to get an NPC invite, you need to go to the Dance Floor by clicking that link after you have been invited by somebody. Or you need to click on the event you get when someone takes up your dance invitation.

Thank You

you are welcome.

Is there a point to the invitations and using them past getting a single achievement for dancing with Abigail?

yes, there's a point. If you look at the bottom of the screen when you dance with one of the NPC Gossips, they reveal information to you. This is not the gossip that they were saying last year in the Blowing off Steam thread, nor is it the same as what they said when the Invitations were last generally available, during the last Atebus plot years ago.

You [str]might[/str] SHOULD find it interesting.

Does anyone know if it's possible to find invites if you're accessing the site from a tablet computer?

My guess would be no, just based on the fact that I've been doing ALL my dancing on iPad so far, and haven't gotten a one. But I don't know for sure.

My girlfriend uses my iPad for dancing/Subeta, and she's gotten invites. So keep trying. :)