first of all, having to post in a forum for a purchase issue? Thats some seriously low quality support right there.
I purchased the tavern pass after my previous one expired(more regret than usual) and its given me absolutely none of the advertised rewards. checked purchase history and bank account and the payment is there on both.
I think you’ll get a faster and better response if you open a support ticket on the battle.net website. You don’t need to post here to get it fixed (just to report the bug exists), it happened to me a couple seasons ago and they were able to fix it after I opened a support ticket. If you go to battle.net and click the Support in the top right you should be able to open a ticket. Good luck!
Do you mean battlegrounds pass? Does it show that you have purchased the pass in game?
Rewards are not given immediately. You need to gain XP and then unlock them in season rewards page after you gain levels.