That out is not natural in the English sentence, but it's important in the Hungarian one. This discussion might clear it up how prefixes make verbs perfective.
The situation here is similar as in that sentence, but ki- is used here instead of be-. It implies that the airport is not in the city centre, so you have to "come out" of the centre to get there. But this directional meaning is only secondary in both sentences, the main function of the prefixes here is to give the verb the perfective aspect I talked about in the discussion I linked.
to come out to can also be natural in English. It means the same as you mean in Hungarian. Usually, "coming out" from a city, a building, so on; to a rural area, or to the outside.
He is coming out to the farm today Many people are coming out to the street I am coming out to the parking lot
It simply means they come to the airport. Some kind of prefix is needed to make the verb perfective, so that it can express that the action has a result: the students will end up being at the airport. "Ki-" here most likely implies that they "come out" of the city centre to where the airport is.
Because they end up at the airport (or as Hungarian puts it "on the flying field" - squares/fields are flat so you stand "on" them) in the sense of within the airport building; not merely next to it / at it / by it.
So you use the ending meaning "onto", not the meaning meaning "to next to".
Not particularly. For gietting out of buses you would say lejön or even more likely leszáll, since you're travelling "on" a bus in Hungarian (a buszon).
You could use kijön with a car, but it's more likely that the students just came out of the city (maybe with a bus) and are going to the airport outside of the city.