"How old am I?"
Translation:Hány éves vagyok?
Part of speech, as in "noun", "adjective", "adverb", etc. The Wiktionary entry itself doesn't include any senses that seem to fit the usage pattern for "hány éves". I've asked there as well, on the Talk page for the term.
As I noted there, the oddity is that the Hungarian expression uses a number-based question word -- hány, "how many" -- but applies it to what seems to be an adjective, which describes a quality and cannot have any number (only countable nouns can have number of the kind needed to satisfy "many-ness").
There are a lot of useful information answering your questions on the "Basic 1" lesson's "Tips" section. You may need to use a browser for it, not sure.
tldr: while hungarian does have a verb for "is", but we tend to leave it out. That is what happens on third person singular, so "hány éves" becomes "how old is he/she/it". And the "vagyok" is the first person singular "am", so it is the "am". Hungarian is also pro-drop, meaning that many times the personal pronouns are left out.
@Albert555583, "pro-drop" is a term used in linguistics to mean that a language tends to drop the pronouns. If you're at all familiar with Spanish, that's another example -- the verb already contains enough information for listeners / readers to understand the person being referred to, so the pronouns become optional.
- "Yo soy..." = "Soy..."
- "Én vagyok..." = "Vagyok..."