iOS 6 short battery life and disappearing storage space (Other increase until it consumes all available space)

I upgraded my iPhone 4s to iOS6. My battery life has decreased significantly I also suddenly ran out of storage space. I plugged into my MacBook Air and noticed that "Other" was about 7 GB. After some Google research, I used the "Reset All Settings" feature. When it completed I had 6.5 GB of available space.

I began monitoring my storage space and at the rate of about .6GB/20 minutes the space is being used. None of my app storage space usage is increasing with this (I made a list).

As another note, I use Google Apps and can't add a second account and my default account rarely, if ever works with the built-in Mail app.

I'm wondering if these two issues are related.

Any clues?