How would you differentiate "Do you have a key?" vs "Do you have YOUR key?" Would it be "Neked van a ti kulcsod"?
No, not like that. In that case a different sentence is used. "Is your key with you?"
"Nálad van a kulcsod?" - Literally, "Is your key at you?"
"Nálad" means "at you", second person singular.
You may notice the "nál" part in "nálad". It is not a coincidence that it matches the "-nál" suffix used with nouns. And the "-ad" part is like a possessive second person singular suffix.
That's how it is done.
You can also say literally "with you":
"Veled van a kulcsod?" - Is your key with you?
"Veled" means "with you", built on the same pattern as "nálad" above. There is a matching "-val"/"-vel" suffix for nouns, that means "with".
You can also say: "Megvan a kulcsod?" It means you have it, you got it, you know where it is, as opposed to it being lost or you not knowing exactly where it is.
Back to your question, "neked" is second person singular, whereas "ti" is second person plural. It would be "te" instead ("ti" goes with "nektek"). But it is totally unnecessary in this sentence, as all two other significant words already imply the person: "nekED" and "kulcsOD".
- When it is indefinite, you can use "neked van", with "kulcsod".
- When it is definite, you use "nálad van" / "veled van" / "megvan", with "a kulcsod". The only thing you can't use is "neked van", because it is inherently indefinite.
You can also use the above definite options (except "megvan") in an indefinite way:
"Nálad/veled van kulcs?" - "Is there a key at/with you?", "Are there any keys at/with you?"
Notice, it is not "kulcsod" here, just "kulcs", any "kulcs".
"Megvan" is kind of inherently definite, so you only use it with definite keys.
When we are not talking about your key, just "a key" or "the key", these are the options:
"Nálad van kulcs?" - indefinite
"Nálad van a kulcs?" - definite
And many variations. I do not want to write a novel... Here are a few valid sentences, feel free to analyze:
Nálad van kulcs? Van nálad kulcs? Kulcs van nálad? Van kulcsod? Kulcsod van? Neked van kulcsod?
Nálad van a kulcs? A kulcs nálad van? Veled van a kulcs? A kulcs veled van? Megvan a kulcs? A kulcs megvan?
Nálad van a kulcsod? A kulcsod nálad van? Veled van a kulcsod? A kulcsod veled van? Megvan a kulcsod? A kulcsod megvan?
Thank you! This (plus a few Fight Club quotes) is exactly what I just asked my Hungarian friend and he could not quite articulate.