Is it possible to make a short-circuit detector for a battery power supply?
My first reaction is to do this more carefully than what others have suggested, especially since it seems you are intending this as a real product.

I'm thinking of a power supply module that you put a bunch of AA batteries into, which then provides reasonably regulated 5 V via a buck regulator.  You may be able to find a off the shelf buck regulator chip that can also do current limiting, but I'd do this with a micrcontroller since you want a bunch of other features.  The micro would be driving the buck switch from a PWM output, and firmware would provide the closed loop voltage control.  The firmware would also be watching the current and doing the current limiting.  Since it knows whether it is in voltage regulation or current limit mode, it is easy for the firmware to light a LED and drive a beeper during current limiting.

The micro would be regularly measuring the battery voltage, and provide a battery-low warning.  I'd probably have a green LED dimly lit when the unit is turned on, and have it flash when the batteries get low.

One advantage of using a buck converter is that it would actually not draw excessive current from the batteries when the output is shorted.  This unit would be quite robust, with little a kid can do to hurt it.

As for detecting multiply supplies chained together, that's not possible soley from inside one of the supplies.