1) The Court of Owls weren’t introduced in either of the Arkham games or the Arrowverse, so they aren’t introduced here either. 2) Yes. 3) This show would explore Barbara as a college student in Blüdhaven, with some nods to the past but not everything translates from the comics to the screen. 4) She was captured by Black Mask’s men. 5) Helena would be in her 20s like in Arrow. Laurel would be in early 30s.
She probably wouldn't appear as much as she did in this first season as there isn't a whole lot of story for her going past season one, but I do love the character and her relationship with Kara so I'd probably have her appear a few teams each season.