The first time I came across the word "milyen"
I heard something like "Mi embuszt keres?" and I was thinking it's "What is looking for an M-bus?" or whatever an embusz would be, lol.
:) Yes, I guess the "ly" sound is naturally not very audible in this neighborhood. But it is definitely there.
Yeah, /j/ is a little bit hard to hear between /i/ and another vowel unless it's pronounced quite tightly.
I think in this case you would use "hányadik buszt keres". Hányadik is specific for a number, 14th, 35th, 1st, etc. I believe if you going by colors or attributes such as yellow bus, orange bus, big bus, etc, you would use melyik buszt keres "which bus"
Even more specific here. If you're asking for a bus number, you say "Hányas buszt keres?" Hányas is asking for the number on something. Bus or tram lines, the number on the backs of football players, document numbers. The answer is a number of the same format, ending on -as/-es or similar: egyes, kettős, hármas, négyes, ötös, hatos, hetes, nyolcas, kilences, tízes, and so on. Note how you say "bus ten" or "the ten" or similar, and not "the tenth bus".
Hányadik, on the other hand, happens when you sort things, 1st, 2nd, 3rd, and so on. Runners, American streets, or everything that you set up in a certain order. The format of those numbers is (mostly) ending on -edik or -adik: első, második, harmadik, negyedik, ötödik, hatodik, hetedik, nyolcadik, kilencedik, tizedik.
As for the difference between milyen and melyik, if you ask "what kind of" (milyen) thing you're looking for, you're looking for a general quality. Fast, red, big, small, Belgian. You don't really care about the specific thing, is just has to have this quality. On the other hand, if you ask "which" (melyik) thing you're looking for, you want one specific thing (or one specific group). The red one, the fast ones, that one over there.
i am not sure, what could be an answer to this question (what kind of bus...). could it be "a small one" and similar answers?
Yes, something like that. What quality are you looking for in the bus? Small, red, fast, double-decker, what you got.
How can we tell the gender? I put "what kind of bus is he looking for" and it was counted wrong. Feel like I am missing something.
Hungarian is gender neutral. You only know gender based on context or if it specifically says férfi, nő, fiú, lány, etc. The pronoun ő means he/she/it. You probably only got it wrong because they didn't add "he" as a correct translation yet.
Can "keres" be second person as well as third person? I translated the sentence as "What bus are you looking for?" and it was accepted.
Usually you would explicitly put in the Ön (or maga) in - but not always.
Yes, keres can refer to "you" formal. Informal would be keresel (indefinite form)
Why a translation in the simple present is not accepted? I translated "What kind of bus does she look for?"
It's an okay translation, but it's rarely used in English. "Looking for something" usually is a one-time action (you don't look for something repeatedly), and one-time actions mostly use the present progressive tense.