Stamina is the resource that is used in the game for all actions. Not only battle, but also mining. It is represented in the game with the blue bar. Every special attack costs stamina, that is why in the battle menu these attacks are in the stamina tab. If that makes no sense for you then I'm sorry, but that wasn't really an issue for other players. In fact, you're the first one who brought that up.
You can't speed up the scenes in android. The port is kept very simple, it is a basic port of the windows desktop version. The scenes end when you press your finger on the screen. I think every android user is capable of figuring that out. Speeding up the scenes only works in the windows version because of the way android handles input variables.