Why is "milyen" appropriate here instead of "milyenek" (since "vonatokat" is plural)?
I believe it's because it is directly describing "vonatokat", which already is plural, so you use "milyen".
In Hungarian there is no "multiple plural", so "milyenek vonatok" is incorrect, while "milyen vonatok" is correct.
Milyen vonatokra vársz, pirosakra vagy feketékre? - should also be accepted.
My answer as well, it's accepted now.
What is wrong with my answer: Milyen vonatokra varsz, pirosokat vagy feketeket.
My first answer that I wrote out of indecisiveness... :D It's actually not right though, you should settle by one type of argument to use. If you decided to use várni +-ra/-re, be consistent and say pirosakra vagy feketékre.
Why is it wrong to put "vársz" as first word of the sentence? Is it because the question word must be first?
The question phrase must go in front of the verb.