nope. Generally the circuit is broken when the bulb goes bust or is not screwed into the socket.
Nope. If your device has no stand-by mode, then it doesn't consume any power if off. But if your device has even a tiny LED light to show "power" then it consumes power (just a little bit).
Nope, the act of turning on your A/C only consumes a small spike of power. The problem is you might be stressing the A/C's mechanical parts than you should be. Normally simply adjusting the A/C's thermostat to a comfortable level and turning it off for the last 30 to 60 mins before leaving the room would be enough to save you a lot of watts.
Some A/Cs already have a "double" plug where you can plug in an electric fan so the A/C's built-in timer will turn off the A/C and automatically turn on the electric fan to keep the cool longer with less power.