Yea that is a swivel. They sell them in various sizes at any place that sells fishing equipment.
For bow fishing I think that you could get away with considering this as a form of archery even if it is not a conventional form of archery. They allow a bow of any weight of pull, and allow long bows and crossbows so why not a sling shot?
You could find a game warden or something just to be sure but as long as you have a fishing license, call it bowfishing and i doubt there would be any problem with it.
It might not be legal for medium sized game, but I have seen video of someone taking a wild boar with one.