There is no confirmation at this time, but it’s possible.
Yes, you can play Super Smash Bros online with other players. You’ll need a Nintendo account and an Internet connection to do so.
No, Super Smash Bros. is not on Xbox 360.
Unfortunately, you cannot play Super Smash Bros. without Nintendo online. The game relies on the service to function properly.
There is no definitive answer, but it seems unlikely. Nintendo has been focusing on new hardware and games for the Switch since it was released in March, so it’s hard to imagine them dedicating the resources to another Smash Bros. game at this point. That said, nothing is impossible and Nintendo could always surprise us!