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1. Yes, if the hybrid battery and system fail the vehicle will still operate.
2. You wouldn't be able to remove the hybrid battery and have the system still work. The battery needs to be in place and functional for the system to work.
If you've had the battery replaced twice then you likely have an updated, redesigned battery now. There were some problems with these batteries and they have been redesigned, a new replacement battery now should last much longer.
As respect answer number one will the car continue to operate or will the 12 volt battery run down and then the car quit. I read some where that the 12 volt battery is charged by the hybrid system and after that fails the car will only operate for an hour or so until the 12 volt battery goes dead.