Hi There,
The TL431 is a precision shunt reference and indeed, in this configuration it acts as a precision 2.5V reference.
The 5V supply is referenced to the positive output through R1. If the other resistors have failed, this one may have failed as well. The 5V supply is superimposed on the positive main supply, otherwise you will not be able to regulate down to 0V. The voltage regulator (top right opamp) will regulate the positive output of your supply in such a way that the voltage on it's negative terminal (= positive out + 5Vfixed -2.5Vref) is exactly the same as the voltage on it's positive terminal (=voltage set by potentiometer in voltage divider between positive out + 5Vfixed and negative out).
I do not know why D12 has shorted though since it is in a high impedance path, unless you shorted the supply over a high inductance load. In that case I would recommend adding a snubber or MOV on the output once you get it repaired. Warning: such a protection device may cause the supply to respond slower.