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No, the power drawn by the amp is a function of the power being sent to the speakers alone, it has nothing to do with the gain setting. If you're playing at 90dB, the amp will be drawing the exact same amount of power from the electrical system whether you have 5V preouts and the gain all the way down or .1V preouts and the gain all the way up.
12.5V-12.8V with the car off and 13.8V-14.4V with the car on is normal, the only way to tell if you've damaged the battery is to compare the capacity now to when it was new (draw a set amount of current, time how long it takes until the battery has reached ~10.5V)
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