I do not see Dragon Arts and Lost Arts on the list, do those also count for points like a building a building would? I dont see a response to this am I in the wrong thread?

This is a dumb question, but if I use a boost to break an item during the brawl, do I still earn the points for the amount of time the booster is worth, or do I have to wait out the break fully?

E.g. a 1 hour booster should be worth 12 points in the brawl

yes you get the credit for the time it would of taken when you use your boost.