A:AnswerMy guess is that it will not help your situation. The only benefit I see is that the Mophie is stationary and unlike a charging cord it does not move causing a poor connection. If the pins are broke there is no contact and as a result the Mophie would not be any different that a charging cord.
A:AnswerSimple answer, no. It is a separate regular charging battery. However, with this case you really shouldn't need to charge your phone during the day. The added battery life is considerable.
A:AnswerYes it will work. It comes with an adapter (small audio cable) to extend the headphone port. The charger port is in the same spot just flipped over. I like charging the phone with the mophie charging port that way you will save the wear and tear on the phone charging port.