We have been taught that ten past two or a quarter past two is British. Americans tend to say ten after two or a quarter after two.
I wanted to make sure if this assumption is correct or Do some American use past instead of after?
Yes, I can attest that several of my family members and their friends, all Americans, do use past instead of after. These people are mostly old enough to have grown up using analog clocks & watches. My own kids, all of whom are under 30, never say “a quarter past/after.” It’s always 2:10, 2:15, etc., as if they’re reading the numbers on a digital clock.