To understand the circuit, notice that there are two different ground symbols used. The 0V "ground" that of the control circuit is just that - the control circuit 0V and nothing more.
The chassis ground, or the mains earth ground is totally separate and is isolated from the power supply output.
From outside the power supply, the control circuit ground means nothing to you at all.
Now to explaining the circuit a little.
First, the control system has its own power supply. That makes design much easier - you can change the voltage at will to to main supply without any affect on the control circuit. You can measure the voltages across a current sense resistor and have the voltage of the sense resistor right at the 0V potential of the control circuit (there is a +/- supply for the control circuit, so 0V is in the middle).
Secondly, the thing that the control circuit is doing is controlling the base current of a NPN power transistor that is at a potential of about 0.7V above the output potive rail voltage. So if you choose the positive output rail as the 0V point of your control circuit, driving that pass transistor is simple.
Thirdly, if the control circuit has its own independent supply, and is has its 0V at the positive output rail potential, it is easy to scale the supply to any output voltage you want. This way, they can take this design and tweak it a bit to be a 30V supply, a 60V supply, a 100V supply - whatever they want. You will probably find that this supply is part of a family, and if you get the schematic of the 30V version, you may be able to just change the components of your supply to make it 30V. That will include needing a new transformer, new mains filter capacitor, perhaps a new power transistor and the output current will be half that of the current supply. You probably have to make a new meter scale ..... Is it worth it? Probably better of selling your supply on eBay and buying the model you want.
Now to your questions. The pre-relay circuit is a comparator with input connected to the positive output. The other input goes to a voltage divider that has one end connected to 12V above the positive output, and the other end to the negative rail. When the voltage across R35 is less then the supply output voltage, the relay turns on halving the voltage from the transformer. This will happen when the supply is below 15K * 12V/24K = 7.5 volts out.
The current control has one end connected to the more positive end of the shunt. The other end of the shunt is of course control circuit ground. The other current control opamp input goes to voltage divider that has one end at control circuit 0V (the output) and the other end at a reference that is 2.4V above the output. So when the voltage across the shunt equals the voltage on this divider, current limiting starts.
Why did they pick the positive rail for control circuit ground? They actually could have picked the negative rail and used a PNP power transistor or a P-Channel power MOSFET. They chose a NPN power transistor and the positive rail because NPN power devices and better, cheaper and more plentiful then PNP power transistors. That is the only reason.