lol. Props on the mower, just dont let them work on it! Get a buddy, push on the brake pedal, have the other person open the bleeder screw. ONLY PUSH THE PEDAL DOWN HALFWAY. Pushing the pedal down all the way can damage the seals in an old master cylinder. WHen the pedal is halfway down, have the buddy close the screw. Then release the pedal, repeat this process until the pedal feels nice and hard with the engine off. Make sure to monitor the brake fluid level while doing this so tha tyou dont let the resevoir go dry.

As for the pad only touching 2cm of rotor, what exactly do you mean? I don't know how to picture that.

a problem with the pads or caliper can cause a soft pedal, depending on the situation.