1. With the common ability dice, if I roll their action symbol can I only use the ability on my turn? Or can I opt to use it during my opponent's turn instead?Any unused Action dice go to Used during the Cleanup Step at the end of your turn (unless they are Continuous dice placed into the Field Zone). There is (currently) no way to save/use an Action Die on your opponent's turn.
2. For things which require generic energy (like most global abilities), can I pay using the normal energy types or can they only be payed with generic energy?Nothing "requires" generic energy. The cards using that symbol just mean X energy of any type.
3. The rulebook says that at the beginning of the turn all unused dice in the reserve are put into the used pile, but the playmat I printed out (from wizkids) says that unused energy is put into the used pile at the start of the turn. I'm assuming the book is correct and the mat is wrong, but I wanted to confirm.Both are basically the same. Unfielded characters go to Used at the end of the Main Step, and unused Action Dice go to Used at the end of the turn during the Cleanup Step. The only thing allowed to remain in your Reserve Pool during your opponent's turn are energy dice (to potentially pay for Globals). At the beginning of your turn, any that you didn't use go directly to Used.
Finally, not really a rules question but why does it matter that energy spent on your turn is put "out of play" and then moved to the used zone later?There are a lot of abilities that allow you to do stuff with dice in your Used Pile, including potentially being able to reroll and use them. The intent is basically that you can only "use" a particular die once during your turn, if you rolled it as energy or as an Action.
Important to note that "out-of-play" doesn't exist (currently) on your opponent's turn, enabling some interesting "infinite" combos.