i had this same problem installing mine. As for the car not shutting off with the ignition switch, I started over.. slower and read everything step by step and that problem was fixed.
For the clutch having to be pushed down, find online how to bypass the clutch with the remote start... If I can find what site I used ill post it on here, if not just look around.
dont scrap the idea! its so badass to have remote start on your car, just think about it... you and your girl are out at dinner but are just leaving, tons of people are waiting in line to get in to eat, you start your car (everyone looks because you have a nice exhaust AND mustang), unlock it and open your girls door. Look at the people looking at you while you walk to your side of the car... dammmnnnnnn baller!
look for this!
1) look behind the clutch pedal, there should be a momentary switch that is depressed when the clutch is pushed down
2) there is a wire harness coming out of that switch, take the harness off of the switch.
3) the harness should have two wires, attach them together and the car will start without having to push the clutch.