It turns the sentence into an interrogative sentence:

• In the beginning of a sentence, it turns the sentence in a yes/no interrogative sentence. Usually you translate the sentence starting with "Is, are, do, does", (p.e. क्या वह तेरे घर में है? > Is he/she in your house?)

• In the middle of a sentence, it turns the sentence in interrogative and it means "what" (p.e. वह क्या तेरे घर में है? > What is in your house?)

A yes/no question marker (this is the meaning when a sentence starts with क्या)

Kya means is

I think that the में transforms the object घर in oblique case, which requires तेरे.

You can (and even probably should), but in the oblique case here, so "tumhare" instead of "tumhara". I don't know about the exact usage of "tu" and its corresponding possessive pronouns in Hindi, but in Urdu they are not used except to show disrespect towards someone, as during a fight for example. Thus the Pakistani address their close friends with "tum", not with "tu".

I think that becomes something like: “What is Neha in your house?” then. Here having क्या first in the sentence is a yes/no question marker as zeebo7 mentioned before.

It’s common to drop it entirely though and rely on the tone of voice, but it’s probably best to learn the proper form first!

तेरे घर में क्या है? should be "What is in your house?"

You mean मैं (personal pronoun, "I") and में (postposition, "in") ¿?

Where did you see a मे ? I don't know this word.