"There is an atrium in the house."
Translation:Atrium in villa est.
If you wrote "in domo" or "in domu", you'd be wrong, because domus takes the locative (using genitive to indicate location), so "in the house" would be "domi". The word domus is extremely irregular (has two different sets of declension and can be msuculine OR feminine, plus it can take the locative), so I understand why it isn't taught here.
As far as I can make out, an atrium was not limited to the villa, but was also found in town houses, at least in those of the wealthier classes. Such houses were known by the term domus. This noun is declined in a somewhat irregular manner, which is perhaps why it hasn't been introduced in this course as yet.
I'm afraid that doesn't answer your question about casa. My impression is that this is used for smaller dwellings, presumably of a type that would not have an atrium, but someone more knowledgeable than myself may like to correct me on that.