"My bedroom is close to the street."
Translation:غُرْفة نَوْمي قَريبة مِن اَلْشّارِع.
I think you're confusing two different things. The alif waslah represents the fact that the alif is not pronounced because of a preceeding long vowel. The solar letter causes the preceding lam in the article to be assimilated, and it is represented in writing by a shaddah (doubling mark) over the shin.
First, ghurfi is wrong anyway. My room is ghurfati.
When you have a genitive construction (yes, nawn is genitive here), this genitive is defining the first word. Therefore, you cannot have a definite article or possessive suffix on the first word (ghurfa). Instead, the possessive suffix goes to the last word (nawm -> nawmi).
I'm pretty sure this answer is wrong. The right answer would have a fatha fawl the noon in "min" and a wasla above the aleph in the next word.
That said, that seems like a pretty Advanced grammatical concept to be teaching in this basic course. So I wouldn't worry about it too much if you missed it.