exactly, as a classifier, it is used for professionals, experts.
- nhà báo: journalist/reporter
- nhà văn: writer
- nhà thơ: poet
- nhà toán học: mathematician
- nhà khoa học: scientist
ngôi is a classifier indicating structures, buildings, markets, graves and stars.
you could have used "căn" (indicating houses and rooms), "toà" (indicating large constructions, such as buildings, temples, palaces, etc.), or the general "cái".
Why is there a "của" in THIS sentence for MY HOUSE, but in the previous sentence, it just said "nhà tôi" (not nhà của tôi)??
For family members you can use "của" or not. I think for other kind of words too (for example for the communist party they say "our party" without của. I'm not sure when it's optional, but i guess it is when you could say also that you belong to it (i.e. you belong to your family, your house, etc.)