Is 'sin' supposed to be pronounced with a 'sh' when spoken fast? because that's what I am hearing.
sin should normally be pronunced that way when it appears after a word ending in an r. We usually assimilate r + s over word borders too. (some dialects have special R:s and don't do this, but Standard Swedish does).
Yes, but the meaning is different: your translation would mean he writes some other guy's name, whereas "sin" means it is his own name that he writes. English is actually ambiguous in this case, so either could be a valid translation from the English.
What does this sentence mean? He writes like his own age, he writes his age (on something)?
Pls sby answer this, it's a little weird and anyone might think it's just a random Duo sentence-
In "Han skriver sin ålder", sin can only refer to the Han in the sentence.
The other way around, "He writes his age" can be translated to either "Han skriver sin ålder" or "Han skriver hans ålder" depending on what person his is referring to: the He in the sentence, or some other person. Swedish is less ambiguous in this case.
When the possessive (his, in this case) refers to the subject of the sentence (He), it switches from the gender-specific ones to the generic sin, which is gender-neutral. Think of it as meaning "He writes his [own] age."
This is covered in the Tips & Tricks section of the pronouns lesson, which you may have missed if you're using the app (the section is only visible in a browser).
If I've made any errors here, feel free to correct me. I'm not a native speaker and can only repeat the knowledge I've gained from Duo.