I always charge with the device on. On occasion, I will Bump Charge the battery. Once the phone is charged and the light is green, keep the device plugged into the charger and power off the device. The light will return to orange showing it is charging. Once green again, you are then Fully charged.
If the phone is off, it will not ring. Anyone calling will be sent to voicemail.
The extended battery for the TB is $60 on VZW and $24 on Amazon. I love the extended battery, it is physically bigger than stock battery but I still like it.