Translation:Where's your house?
The northern Chinese dialects, especially the Beijing dialect, likes to add "er" sounds to the ends of words, represented by the character 儿 . The name of this process is "Erhua" (儿化), and 哪儿 is just the erhua version of 哪里.
I was wondering the same thing; Seems like it's mostly a dialect difference, with 哪儿 being more common in the north, and 哪里 elsewhere? With some footnotes and caveats in more advanced usage? This is what I could find: https://chinese.stackexchange.com/questions/9131/%E5%93%AA%E5%84%BF-vs-%E5%93%AA%E9%87%8C-difference-in-meaning
That wouldn't be the best translation. "Where do you live?" would be 你住在哪里？
Exactly, while you might live in a home they are not the same. For learning it's best not to mix up nouns and verbs.
Also having 家= house is not quite right and can cause confusion. 家= home and 房子= house.
Can you provide a sentence where 房子 means “room” (房间 or just 房)? I never saw it be interpreted that way.
I'm not a native Chinese speaker, so I'm just going by what I've read while studying the language. But I've seen 房子 be defined as "room" before. For example, Wiktionary includes this as a definition (https://en.wiktionary.org/wiki/%E6%88%BF%E5%AD%90) . It also gives an example sentence: 我在找一间正待出租的房子。("I'm looking for a room to rent."). But I assume that 房间 is a far more common way to say "room", yes?
Yes, 房间 is rooms in general. 房子 can mean the rooms for rent specifically (edit: more exactly, a set of rooms on the same floor of a flat, which can be rent or purchased), but we need more concrete context.
No, that would be 你的家在那里吗？. Remember: 哪里 is "where", and 那里 is "there".
你的家在那里 and 你的家在哪里. How do you differentiate these two when spoken?
家 = home, 家庭 = family (the social structure), 家人 = family (members)
If the 的 is taken out, then 你家在哪里 can be interpreted as “where is your family?” in this scenario: Your family is having a picnic and you meet a friend who is also having a picnic with his family.
你家 can mean “your home”, “your house” or “your family (the social structure or the group of members)”.
你的家 can mean the first two or “your family (the social structure)”. It just feels wrong to interpret 你的家 simply as the group of family members. Maybe if this phrase keeps repeated enough for family members I will accept that 你家=你的家.
那 = that/those, 哪 = which/what. For example, 那个男人吃米饭 is "That man is eating rice", and 哪个男人吃米饭? is the question "Which man is eating rice?" In spoken Mandarin, the only thing differentiating the two characters is tone...so be careful which one you use! :)