Did this start happening all of a sudden? Or has it come on gradually? Any recent repairs/improvements made?
Assuming no vacuum leak, check electrical grounds. Also check to see if carb float and fuel shut-off are working properly. If float goes up and sticks, fuel to engine is shut off and engine quits running.
Probably not. Should be open if engine is at operating temperature. If you notice black smoke from tail pipe at idle, then maybe a choke opening problem.
The key??? You won't lock up the transmission or steering just by turning off the key. If you put it in park while moving and turn off the key, big problems. If service brakes don't work, use the hand brake. Twist and pull. If rears start to lock push in. It is easier to modulate the rear brakes if you don't pull the handle out straight without twisting it. Suggest practice in a large, empty parking lot so you'll know what to expect. Start idle speed and work up, unless you're into thrill seeking.