Yes, it does have to do with the qactuar stones The more you pray to them, the more qactuars will show up when you encounter them. They have to do with something else, but i can't think what-- there's cobwebs invading my mind xD

Fafnir is the dragon-dog-not-little-dog monster arena boss, right? I think you'll probably run into more of those on the north side of the thunderplains- try sticking around the little gazebo out there.