Critique for my short circuit indicator and guidance to improve it
Very nice circuit!

To answer your questions:


This circuit is not able to replace a fuse, because it does not protect in case of a short circuit, it only gives a warning. Your diode D2 still needs to handle a forward voltage of 12V in case of a short circuit and will break as a result.
As a solution to this, you could think of a circuit that turns of your power supply to the load, whenever the load is short circuit. Or maybe even safer. A circuit with memory, that turns off the power supply when the load is short circuit and until a button is pushed stays off. 
To adapt this circuit for a negative power supply, you could connecto the 0V to the location of your current 12V and the -12V connection to your current GND connection. You might however want to have the diode not in the GND connection, and move it in the path of the -12V supply. In that case your diode D2 would forward from D5 and JP1 to your  -12V supply, and you could leave out the inverter made with Q2 and R1.
What kind of transients do you mean here? Short over voltage of your 12V power supply?