Kiszáll and leszáll can (and most often do) refer to unboarding a vehicle, just like beszáll and felszáll mean boarding one.

Ki-/beszáll are used with vehicles that get -ba/-ban/-ból suffixes, so this example is likely talking about getting out of a car.

Yes.

The ki here is a verbal prefix. It's an odd name, since it's clearly behind the verb, but in Hungarian verbal prefixes can do that. Ki defines the direction in which the száll happens. Ki usually means "outward", so kiszáll means "to get out (of a vehicle)".

Nem wants to be in the focus in this sentence, do it displaces the verbal prefix and pushes it behind the verb stem. Without the negation, this sentence would be. "A gyerekek kiszállnak."