Actually heating the cage from the bottom is the best way to provide the appropriate heat a ball python needs. The problem you encountered is because all heating elements need a control. A thermostat or even a dimmer will work to adjust the heat output. A digital indoor/outdoor thermometer will help to ensure that those temps are achieved. (plus they measure the humidity as well)

A pinky mouse is awfully small, even for a baby bp. It may not had to poo because there was no excess material to excrete. It's possible that bp also had internal parasites and may have led to it's demise. It sounds like you may want to find a new vet that specializes in herps. They should be able to do a fecal and sex the snake for you.