"Are you going to his house?"
Translation:Ĉu vi iras al lia domo?
Is "Ĉu vi iras al lia hejmo?" correct too? If not, what is the difference between "domo" and "hejmo"?
domo is a house and hejmo is a home. One is general or formal and the other familiar or personal.
"iranta al lia domo"
Granted, coming back to this after the change over to crown system but I cannot for the life of me recall iranta as a familiar verb form
"Estas iranta" is the present progressive form of the verb. "I go to his house" - "Mi iras al lia domo"; "I am going to his house" - "Mi estas iranta al lia domo". In regular conversation you'd just use the simple tense though, unless you wanted to emphasise that you were in the process of going right at this moment. Progressive verbs are dealt with later in the course.
I thought 'iros' on my first time through. Sure, 'going' is present tense but at least where I live people say "Are you going..." all the time when what they mean is "Are you going to go...". For example, one might ask "Are you going to the party?". They likely do not mean "are you presently on your way?".
It's hard to imagine someone really meaning the present tense when they say this. I'm imagining someone sitting on their couch and someone else walks up and asks if they are (presenty) going somewhere. Sure.. it's a magic couch that just makes it look like you are sitting still while it whisks you off to a magical land. Stop talking to me, I'm not really here anymore. Or.. running alongside someone's car and asking "are you going somewhere?" No. I'm standing still! Why are you so out of breath?