3 new problems including sudden increase in battery drain

Hate to say it but that has factory reset written all over it. Could be a rogue app but that is a lot of issues to try to pinpoint.

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I have noticed the decrease in battery life too. The stock rom (and therefore all roms based on it) has a nasty bug with system apps freezing themselves and I am wondering if this is also somehow draining the battery. It seems to be related to installing and uninstalling apps. If you go into the built in task manager, you will see a bunch of flashing before you can do anything.

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If you haven't installed a custom recovery, you can do it right though the settings. It is under the sd card and phone storage menu. You will lose pretty much everything, that is the point of doing it, to return you to the out of the box state. On first boot after the restore, immediately go into the market and cancel the app redownloads. Reinstall them manually, reading the reviews and being careful they are not problem causing.

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No

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Actually you will if they aren't synced to you google account. you can just back up your numbers to your sd card if you want anyways.

 

Seekdroid is a phone finder app in case you lose it. It needs for the phone to be active as much as possible, probably. That's your culprit imo. If you are rooted, just go into system/app and delete the apk file. It's hidden so the thief can't uninstall it.