Adjustable Power Supply with LM317
1) As has been stated in the comments, you will never see 30V across R1 nor will 1A ever pass through it. The voltage across this resistor is about 1.25V.

2) The datasheet should tell you whether, or under what circumstances, you need a capacitor to ground. This information is in Figure 1 of the datasheet I found online.

3) Heat is not measured in tons, and I don't know what you mean by "expending much". Choosing a resistor to use with an LED has been discussed over and over again, on this site as well as others.

4) What does the datasheet for the LM317 say about short-circuit protection? You should find all of the information you need.

Finally, I will say again that you need to revisit your plan to dissipate 30W in this regulator. I don't think this will be possible without "expending much".