The possessive pronoun is not always needed in Norwegian, at least less often than in English it seems. You could say : Grandma is reading the newspaper. Not needing the "my" as grandma ascends to a name of sorts and not just a title/description (as the very lumpy paternal grandmother).
If I tell my two year old son that "mormor lager kake" (maternal grandmother is making a cake) I'm talking of my own mother but his grandmother. The possessive is not needed because there is closeness between the people included in the conversation (if I were to tell the kid next door that grandma was making a cake, I would add the possessive to be sure we both agreed on who's grandma I was referring to, mine or his or my son's), and so far one can have only one maternal grandmother.
I could say either "Mamma lager kake" or "Moren min lager kake" ("Min mor lager kake" is also valid), all translates to Mom is making a cake/My mother is making a cake.
Not if you want to be specific about which grandmother you are talking about
"Father's mother" is a really bad translation, I think. I never heard anyone refer to his/her grandma in such a way.
When making (generic) translations in the Duolingo machinery sometimes you loose certain distinctions. Translating farmor will be difficult as it's a term not used in English, and whose grandmother it is is contextual in Norwegian, it is uncommon to use the possessive. And translating back and forth and getting the exact same result rarely happens. There are several correct answers to farmor leser avisen, two would be "my paternal grandmother reads the newspaper" and "my paternal grandmother is reading the newspaper". But none of them translates smoothly back into farmor leser avisen as the first round generated a "my".