I looked at my outlets today the top is fine but the bottom ones all have a prong broken off stuck inside. I always wondered is this why my electric bill is so high! Please can someone tell me if broken prongs in outlets drain my electricity!!??
A prong by itself cannot make a complete circuit. Even if it did, it would immediately trip your circuit breaker and likely damage the receptacle (as in it would visibly spark/arc). It doesn't sound they they're on the surface either, or they would be a shock hazard.
If I were you, and you feel confident enough to turn the power off, you could replace it easily with a new receptacle. It's just a matter of unscrewing and screwing with wires. Take a picture of the wires before you disconnect them.
I'm assuming US plugs here. No, broken prongs will not cause an increase in your electrical bill. In order for electricity to be used and appear on your bill electricity must move from one side of the top row to the other side of the top row in a circuit, through an electrical device of some kind. If you jumped directly from one side to the other with a wire it could cause an overload and blow a circuit breaker, so that clearly isn't happening, and it would happen so fast it wouldn't add to your electric bill.
The bottom prong is for grounding, which is an electrical safety mechanism, if there's a short in the appliance the energy will go there into the ground instead of through you, so it's very important you get this fixed. You could pull them out, I'd personally be concerned that the outlets have been damaged, which could be dangerous, and I would replace them. If you aren't confident about that type of work do not attempt it yourself.