Okay, so I have the same phone and the same problems.
I now know for a fact that it is not the battery because I just got a brand new battery in the mail and it did not work.
I charge my phone all night long every night, and if I don't use it once, at all, the battery will last for approximately 8 hours, when my dad's will last for 2 weeks.
My sister has the same phone and she is having the same problems.
I also get the dropped calls, and have no idea what causes that...