Are these correct? Trying to figure this out.
HaadhAA SaaloonUN Qadeem "This is an old living room" هاذا صالون قديم
HaadhAL SaaloonUN Qadeem "This old living room" هاذ الصالون قديم
HaadhAA huva SaaloonAL Qadeem "This is the old living room" هاذا هو الصالون القديم
Ah-SaaloonAL Qadeem "The old living room" أصّالون القديم
SaaloonA Qadeem "An old living room" صالون قديم
Mostly a very good job yes, just a couple of remarks:
1) haadhaa is spelt هذا, without the first alif. And الصالون is pronounced aS-Saaloonu, but still spelt with a laam, like you did in the two examples before it. هو is pronounced "huwa," not "huva."
2) In the second sentence, it's "haadhAL SaaloonU," without an N after the U, since the definite article isn't followed by nunation.
3) "haadhaa huwa aS-SaaloonUL qadiim." In the third sentence, don't forget the definite article. You wrote it in the Arabic, but didn't transliterate it.
4) In the final phrase, there's no reason to end Saaloon with an -a. "SaaloonUN qadiim."
As explained in other comments here, for it to be "this living room" you would need the definite article "Al" ال before صالون Because the demonstrative pronoun "this is a thing" only becomes a demonstrative determiner "this thing" if the thing is definite.
In Arabic the indefinite "a thing" is always implied if it's not otherwise defined. You could think of it as "this thing" in Arabic is always implying "this (is a) thing" unless you clarify it as "this (the) thing (is)".
Hope that helps!
I have a lot of problems with this as well: most of the English sentences about living rooms, which correspond to Arabic sentences about salons, sound very weird. I think the issue is that, normally, you can only say, in English, "the living room" (or "my living room", etc.) but not "a living room". This is probably because living rooms are defined by function, and there is typically only one room with that function in a house. Arabic seems to be different (I'm taking it that the Arabic sentences are OK). But I think the English sentences on this course need some attention.
It's all about the definite articles: This is a living room: هذا صالون This living room: هذا الصالون When one word is definite (consider هذا as definite), and another is not, put "to be" between them in the translation. When both are definite - don't.
So in the Erfan's sentence "is" is between "living room" and "old". In the duolingo sentence "to be" is between "This" and "a living room"