There are many people living in the new house - why is this not accepted?
I believe "There are many people..." is good translation for this sentence. Report it.
I think, but I am not sure, It should be "Sok ember van, aki az új házban él/lakik.".
the pronunciation is throwing me way off in separating words aspect
This is what I heard: az ujház van sok emberlakik
I know that "az" is either "that" or "a" (if the next word begins with a vowel). So, would it be ok to say "Lots of people live in THAT new house"? If not how would you indicate THAT house?
Does the Hungarian idea of a house have a broader meaning than the English word "house". If many people live in it it seems like something other than a single family dwelling.
yes. More precisely one can say bérház, emeletes ház, panel ház, they all have many flats. But ház does not always mean a single family home.