The trouble you are having may be due to a problem with the blower speed control module. You may have a solid state unit. It may have failed in a way that allows a current drain through the motor. The module is close to the blower under the dash, mounted on the ducting for cooling. If you disconnect it and find the current draw on the battery goes away then you found the problem to both issues. The modules usually short or open when they fail. If they short then full power is applied to the blower motor at all times. Even when the ignition is OFF. The module is in series with the power line.
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