Unfortunately, no, you may not. Tournaments are already a very XP heavy event.
Yes. Battle Pass is not an all you can play membership, however, Battle Pass members receive a discount on all campaign games.
No. All points, challenges, and bingo cards reset at the start of the new season. The only items that carry over are Materials, Skins, and Badges.
A player banner is a way for you to show off your accomplishments to other players. You may display up to 3 badges of your choosing on any of the frames that you have unlocked while playing.
No. The Discord channel is a tool at your disposal, but you are not required to use it, or even participate in the discussion inside of it. Discord is used primarily to send information to all Battle Pass players first, before it is posted to Social Media, as well as assist players in filling upcoming games.