"Also, do Dragons block Queens as Alibabariders usually move, or can they block Queens on the squares they leap over (As a semi-leaping Queen)?"
As I read it, Dragons have no influence whatsoever on the squares they leap. For example, a Dragon on d1, controlling the line d3-d5-d7-d9, would not stop an opposing Queen moving a6-h6, crossing at odd distance from the Dragon.
"On one other note, why promote your pawns to Knights rather than Unicorns?"
In order to promote to a Unicorn, you must have lost one of your starting Unicorns.