Don't put the throttle cable eyelet on the same pivot as the spring. Separate them like this (not my photo):
I understand your frustration but it's not your fault--you inherited the previous owner's problem as the new gas pedal isn't stock/OEM, was not designed for that kart and neither is the gas pedal return spring. Those springs are chiefly a Manco part but can be adapted to fit.
Don't worry too much about a return spring on the gas pedal or right at the gas pedal -- not all karts have them. They often rely on a throttle return spring on the engine [but sometimes in both locations].
I would straighten out the end of the brake rod; you could do it with two large Vise Grips, Crescent wrenches, Channel loc pliers, or something beefy.
As for the brake band and drum, something is off kilter with the spacing and I cannot figure it out. I better review the photos of the kart when you dragged it home...