How does it differentiate customers? Same question for a couple people checking out together.

Airports already handle this on a daily basis:

Cameras scan only small field.

Will I have to take my hat and sunglasses off to check out or does it use other technologies to build face maps like lidar?

Probably the same as face unlock in iPhones. You can check how this works and apply answers here.

What will it do about age verified products like tobacco or alcohol?

This is just another form of payment so it will do the same as credit card or cash.