Will Serana have any new quests or related content in Dragonborn? She is best character in Elder Scrolls, besides Paarthunax, so i hope we will have at least some continuation to her story (despite it finality in Dawnguard).

Very unlikely.

It's very, very rare that DLC will ever contain content that requires another DLC. In this case, adding content to Serena in Dragonborn would require Dawnguard to be installed as well.

And forcing people to own a DLC in order to play content for another DLC is a pretty low down move, which Bethesda won't do

might be like in new vegas where it might reveal some more info on vampires,dont know why maybe the first dragonborn was very interested or something