"My mother is a cook."
Translation:Moren min er kokk.
In Norwegian, there's two different ways to write "my mother". Option A is "Min Mor", and option B is "Moren min". Both are equally valid, but option B is more common.
As for why this is.... Unfortunately, language does not always conform to our expectations, and sometimes they have unexpected or unusual rules. You'll unfortunately just have to get used to using the definite form when using option B.
"Mora mi" is acceptable, and so is "moren min". You need to match the possesive pronoun (mi/min) to the definitive noun (mora/moren), but otherwise you can use whichever form you prefer.
In the Oslo dialect (which Duolingo teaches), it's fairly common to use the masculine form over the feminine one. As long as you're consistent, you can use whichever you're most happy with.