Any BAT you earn now will be stored in your browser. When payment issues this next month, you should have a Claim button appear in your Rewards. Once claimed, it stores on the browser itself. It can’t be transferred anywhere except to tip Creators.
Yes, it will be back. They are working on bringing regions back little bits at a time. The first back was France, which just was added again yesterday. Next is Brazil and maybe India. Not sure when others will be added again. You can keep track of updates by checking in on PSA: Unsupported Region