Defense/offense knows what to do?
 

NFHS..Defense is responsible for knowing what to do with the ball. Does that apply to the offense knowing if they are out or safe?

BR goes to 1st because of a dropped 3rd strike but she mistakenly thinks it was caught since no play was made on her and the ball was returned to the pitcher by the catcher. She steps off 1st to go to her dugout.

Should the umpire call time, and inform her that she could in fact run, or should he call her out not knowing when she stepped off?

Out. That is why there is a base coach.

hrmmm.. ive read this someplace else... twice.