Regarding the battery, charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:
1. The main Settings>Battery screen.
2. The fullscreen battery graph screen (which shows Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).
http://forums.androidcentral.com/am...ide-how-post-screenshots-android-central.html
Two common causes of battery drain are poor cell signal and a corrupt media file on the SD card. The former will result in high Cell Standby usage, and the latter will often show up as high usage by Mediaserver or by the System.