I went through every variation I could think of giving the adrianna the scroll of banishing (sometimes she won't take it). I either get a ring of vampirism or 'the ring of miiril (?)' (and end up as a vampire or not)

I ask because this part smells to me like the solution to the quest to be a Valkyrie. I ran into several bugs and crashes here and don't particularly want to play it any more.
So I would greatly appreciate it if someone would tell me whether or not this has anything to do with the valkyrie quest. If not, fine; if anything important is supposed to come out of this section, please tell me.

No, there is no connection with the valkyrie quest. No, you don't have to do it at all to complete the adventure. In fact I killed Adrianna and her bunch the first time I met them because I refused their quest. On the other hand you get a nice piece of story and a ring by accepting her quest, without freeing them. But if you've seen the story an are not partial to a ring that makes the game crash when you put it on, you can just as well skip it.

You give Boogre brew to vampires, they not nice and green yet. Perhaps then they friendlier to warm-skins.

Thanks much! Goodbye, Adrianna!