(I fully admit this was inspired by my own story.)
The Time/Device and Skill could probably be used in many ways. Three stand out to me right now.
Speed Up: Can decrease the time of certain things. Like tree or crop growth. Or shorten cool down periods. Obviously these would have to be off set by high energy costs. (Since cool downs are a balancing thing, the potential for this throwing things out of whack might be too great.
Reset: Reset daily limits (koins, tree harvesting, piggy nibbling). Again the cost would have to be big but this would have less of a chance to be game breaking. Also Reset itself would have to have a daily limit (if not a 'weekly' one).
Regression: This could be used to return things to their 'original' state. Piggies into piglets with can be picked up. Or piglets into eggs. Trees into beans. Or meals into their component recipe parts. And, yet again, an energy cost would be needed. Perhaps the device even needs fuel for all this stuff.