A:AnswerYes, the airpod case has a sync button. You would have to open the case, hold the button on the back until the light flashes white, and move it close to your unlocked iPhone
A:AnswerNot sure about the actual stats, but charge the case overnight and it should last you the next few days of charging the pods. The pods are in my ear pretty much all day, then back in the case. I don't remember to charge the case every not, I forget to more often than not. I've never been stuck with dead airpods.
A:AnswerNot at Best Buy. Maybe with their credit card, technically speaking. True monthly payment options are really only through cellular service providers, but that is for the airpods w/ case -- not just the case itself.
A:AnswerI have brought this charger to charger all three of my Apple product from Amazon,. I charge all 3 at one time. The wireless Apple case can also be charged with the wire too