What your asking is for someone to teach you mechanical and electrical engineering and then prove to that all they are teaching you is true. That's a pretty tall order and I don't think you'll get any takers.
I can tell you that the electric motor will produce an output power equivalent to the input power times the efficiency. In this case they claim 13HP but I can tell you that with less than 6 ampere hour capacity this will be for a very short duration. 13HP is over 12000 Watts of power into the motor at 80% efficiency. If the battery can maintain 80 volts under full load then current draw would be in the vicinity of 150 amperes. So, at full load the battery charge has a theoretical life of about 2.3 minutes and I can tell with absolute certainty it will, in real life, be considerably shorter. This is a best case scenario! When the temperature departs from optimum and/or the battery sulfates everything goes down hill from there.