LM317 maximum resistor/pot - Current regulator - Reference voltage
This value is given to maintain the minimum load. It isn't a magical value, pick whatever satisfies the minimum load in your application. 
Using 120R guarantees 10mA but uses more power. 240R is above the absolute minimum of 3.5mA and is probably but not certainly fine.
The latter is the correct datasheet equation.
R1 and R2 form a divider to present the required voltage to the adjust pin. If you want to use a 50k pot instead of a 5k pot for R2, you can multiply R1 by 10 and satisfy the minimum load requirement with another resistor to ground.
The drop depends on the load, see the National Semi version of the datasheet for the graph of input-output differential versus current. If you design for a smaller value than 3V you had better know your load very well.


In your design, when SW1 is connected to R4, the first LM317 has its current limited to about 10mA. This will all be consumed by the second LM317 and R1, leaving nothing available for the load.

You seem to be going for a large output voltage range. You still need to do the thermal design, this project is going to be bulky.