The payouts are calculated in USD, not in BAT. BAT is only used because it is the "easiest" way to send money to users without getting banks from every corner of the world involved. If you want to cash out the BAT, you need to go through the KYC with one of the partner exchanges. But if you just want to use the BAT to tip other users, no KYC is needed.
The ads from Brave are completely private - your browser downloads the whole inventory, the ad-matching is done in-device, and a separate service is responsible in validating double-blind signatures to count for your ad views.