To continue with the story, you need to call the function RenJS.resolve(), this is called after completing every action, and tells the story interpreter that this action is finished and to read the next one. In your minigame, make sure that you finish it completely before calling RenJS.resolve(), for example, you'll need to hide all of the assets, finish all animations and tweens, stop music, etc.
On you're second question, as long as you store your variables into RenJS.logicManager.vars during the minigame, then you can use them in the story as well.