Is it just me or "ngôi nhà" sounds here like "mu nhà"?
Does ngôi act as classifier here ?
yes. it is a classifier for structures, buildings, markets, graves and stars.
Another possible etymology is 舊, and I haven't seen cũ represented by 古 in Han-Nom scripts.
Yes, it is
Ngôi isn't necessary here
Why is je pronouncing old so weirdly?
Where does the translation "that" come from? I wanted to say Who lives in the old house? but it wasn't an option. I don't see any word in Vietnamese that translates as "that."
Why not, "Who lives AT that old house?"