The biggest problem I've had with my Mark VIII wasn't the stereo so much as it was an after-market alternator. I've been thru several from chain parts stores and until I sucked it up and bought the factory/dealer unit, I have ALWAYS had charging problems and low battery voltage. Especially whenever I played my stereo. The after-market units apparently don't seem to communicate with the cars computer properly. If you have an alternator from anywhere else, bite the bullet. It's worth the extra money.
How you fix a tail ligth from killing battery
You may have to disconnect and recharge your car battery for your car stereo to work again.
connect the positive and negative to the stereo
No.
yes, it is possible
The batteries may not be in correctly.
power from the battery
Yes it can.
It depends on the capacity of the battery and the power used by the stereo. To roughly calculate the time, divide the amount of charge in the battery (amps hours) by the amount of current (amps) used by the stereo. If you don't know the current, divide the power of the stereo (watts) by 12. That would give you the current at max power output (max volume).
I think you answered that question yourself, when you said, `hot wire', which usually means the positive battery power lead.
For me the reason the clock and stereo were resetting was because they were losing all power from the battery. The battery was dead. maybe your cables need to be cleaned or there is a loose connection.
When a stereo system drains too much battery power, it is time to add a capacitor. The capacitor will not increase the battery, but instead will modulate it allowing for additional stereo usage.