The suggested translation is just 'Grandmother… ' That works in English too, if you say just Grandmother or Granny, people will probably assume you're talking about your own one.
Since you tend to use the possessive a little more often in English, My grandmother is also an accepted answer. But if we want to be clear about whose grandmother we're talking about, we'd say min, din etc in Swedish too. There's absolutely nothing strange about using the possessives here in Swedish either.
No, it's a matter of logistics. Please see the top question here: https://forum.duolingo.com/comment/20444477/FAQ-for-the-Swedish-course
MAM3166's link is actually for the word skarp. To hear the pronunciation of skärp you need to go instead to https://sv.forvo.com/search/skärp/#sv -- then click on the right-pointing triangles to hear the recordings (ignoring, however, the first one, which is for skarp -- a site error.
For a (very!) full account of the sj-sound (also sk- in front of e, i, y, ä, ö), see https://youtu.be/OvlwXQ1bDvc
It's rather annoying that whenever I write something like "Grandma's buying" (for "Mormor köper") duolingo insists on telling me "You missed a space". Oh no, I didn't!
I didn't "miss a space", because to miss a space is to fail to notice it. And I didn't even "miss it out" (i.e. fail to insert it), if that is what duolingo is perhaps trying to say. No, what I did was use the contracted form of is (which is never preceded by a space). A further oddness is that duolingo doesn't have this problem when I write, say, "She's buying" (for "Hon köper").
Duolingo's admin interface is a little tricky with possessives, since the system tends to create them in its own way. I think I've fixed the default so that "Grandmother's buying a new belt" works as intended without typos, but there are 160 accepted permutations of translations for this sentence, so some other similar variations will probably still yield typo errors.