Go to settings, general, reset, erase all content and settings. Then set it up as a new phone. If you're concerned iOS has been corrupted somehow you can also put your phone in DFU mode and use iTunes to restore the firmware.
Plug into iTunes, press and hold the power button and home button for about 10 seconds (or til your computer makes the usb disconnect noise), then let the power button go and keep holding the home button for approximately 5 seconds. iTunes should detect your phone in DFU mode and take it from there.
Yup!
Well, you could restore from a backup and see if your problem has been resolved to save the trouble of setting everything up again. No idea if whatever caused the problem may be included in your backup files/settings. Did you check your background refresh settings and your cellular data usage?
I'm using on average 1 gig a day even when connected to wifi most of the time.
Which App is using the data?
No idea most of the time it's happens when I sleeping.