Depending on how and where you measure the battery, 12 Volts reading is only about 50% level of charge. A fully charged battery should read 12.6 Volts.
You need to leave your windows and hood open and after you turn off your car, come back after 25 minutes and listen to determine if you can hear any fan motor running. There are 2 fan motors that have issue, the small one in the climate control panel and the main HVAC blower motor.
Doubt your fuel pump is an issue if you have the battery going flat.