Current limiting ( aka constant current generator ) work like this: When some chosen threshold is reached the voltage is dropped so the current chosen can be maintained, you cannot have the same voltage and same current for any load level, let say you have a resistive load of 10 Ohm and an output voltage of 20V, that makes a load current of V/R =>20/10 =>2A, now let say we drop the load to 5 Ohm but we want the same voltage on that new load and the same 2A, well that is impossible cus as we have pointed out already I=V/R =>20/5 =>4A; what then? well if we need the same current we drop the voltage, and V=I*R =>2*5 =>10V. That is how current limmiting works, it reduces the voltage to maintain the current in needed limits.

Any NPN small signal transistor will do as long as the Vce of it it's larger than any espected Vin on the regulator ( that is just to be sure ), it does not need a heatsink cus it will work only when the limit is reached and it will dissipate a small enough power, the resistor indeed would have to be 330m Ohm for 2A limmit and it's power rating P=V*I =>0,65*2 =>1,3W, make it 2 or 3W.

a) It will impact the regulation at any current level...

No, it will not, maybe you should study more of this config... as long as the voltage across the shunt resistor is less than 0,5-0,6V the transistor will not enter conduction, and let say that the load is 1A, on a 330m Ohm resistor will be 330mV, that is too small a voltage to biass the BE of it, so no, only near the threshold when Vbe will be big enough the regulation will be affected.

a) b) On a dead short, the current limit will be double the normal...

The regulator already has internal shortcircuit protection and so it will not be affected, and the NPN will be protected by the base resistor, so nothing bad can happen at a shortcircuit, and anyway nowone will short a PSU just for the fun of it, that can only happen accidentaly so in short periods/time and as i have pointed out it cannot affect the regulator.

..A LM317 is cheap compatible with the LM338, does the job perfectly and won't lead you into troubles like oscillations

There are no oscilations here, both the regulators are about the same, only this one can handle more current, on the other hand LM317 would only giv about 1,5A, and here it is needed 2A, i think it is the best way to go.