Why 'de la'? Why two prepositions?
They're two particles (? don't know if that's the word), but basically "de la" functions as one preposition.
Why is "de la" used instead of "din" ?
La= translated as AT FOR or ABOUT.
As zj456 is asking why not DIN
"din" originates from "de în". I suppose it would sound as if the letter was in the person earlier and it came right out of them. Meanwhile, the letter was just at/by them, as "la" would suggest.
Shouldn't "The letter is yours" be correct as well?
I can't say for sure but I'm curious why you think it would fit. What are you basing that on?
Now that I look back on it I see that it my suggestion actually doesn't make sense