Assuming it's nothing fancy, there should be a wire going from the ignition barrel which goes to the solenoid, when the switch is in position 3 the power is sent from the via the main feed to this.

So you would need to take a feed from this to the push switch and then the original start wire from the switch and connect this to the push switch.

You still need to use the ignition switch and then use your push button to start, it seems pointless to me!

Red needs to be connected to a supply and the ground connected to the door switch, so it completes the ground side, I guess it says to do what it does as old cars have a positive ground.

No, the switch is what is actuated by the door, hence the name.

Martin