(1) Some priests do, and in many Greek texts it is called for. Others do not, and it is not included in the Maroon HC-Edition of the Liturgy book.
(2) IIRC, the prayer behind the Amvon is the older blessing/dismissal of the Liturgy, with the formal blessing/dismissal that follows being a later addition (semi-standardized, as one can see with comparison to other services).
In some places, these are done; in others, one but not the other; in others, neither. I don't think they're "American" per se, though.