Yes, online poker is legal in the United States, albeit only in certain states. As of early 2024, only six states have legalized online poker Nevada, Delaware, New Jersey, Pennsylvania, West Virginia, and Michigan.
Donk is a (potentially offensive) term used to describe a very bad poker player. A donk bet is a bet made out of position after check/calling on the previous street. The link here is that it's usually 'donks' who donk bet hence the name behind the bet.
An up-and-down bet involves two selections and two separate bets on both those selections, in each of which the second bet is conditional on the first one winning.