Does this mean ,,the girl opens her sister's letter,,? And wouldn't then be more correct ,,Jenta åpner brevet til søsteren sin,,?
It means that she's opening the letter that she got from her sister.
If you want to express that she's opening the letter that belongs to her sister, then "...brevet til søsteren sin" or "...sin søsters brev" would be good translations.
Is there a difference in the context of when to use "sin" instead of "hans" or "hennes"?
The girl is opening letter from her sister how it can be correct.
You're missing the definite article: "the letter".
This phrase now seems a little archaic! Who now writes paper letters ?
"The girl opens the letter of (instead of "from") her sister" should be also accepted
Couldn't you also say She opens her sister's letter? Or was just not acceptet 'cause I forgot the ' sister's?