I was awarded a billboard from the bathhouse pools, and I am really confused. What can I do with it? If it's for running an ad, can I sell it to someone else? Please help, I am really stuck on this...

As it's an item of course you can sell it! Just stick it in your shop. c:

It relates to this cash shop page for running ads, although I'm not sure if the items are currently functional.

Yes you can run an ad with it. If it's an item you can sell it to other players.

Alright, thanks!