For the future, please ake a separate topic for each separate bug. That makes it easier to keep the discussion sharp and on point.
For the adventure progress issue: did yu double check that you logged on to the same account, and to the same region? If yes, then please make screenshots of your progress as shown in game, post them (e.g. on imgur.com) and share a link here, and explain exactly what should have been displayed.
For the Arena progress, you probably cancelled out of (or disconnected during) matchmaking. This known issue is described here (Hearthstone Common Issues) and here (https://us.battle.net/support/en/article/17276?blzcmp=app)