At the end of chapter 13 Phillip did two things that prove he is able to survive. What were these things and why were they vital things for Phillip to learn?

Phillip learns two key things in chapter 13. The first thing that he learns is how to fish. He first has to pry mussels off of the rocks, and then he uses those as the bait for fishing. Readers are told that after a few days of practice, Phillip is capable of doing all of the fishing for both him and Timothy. Phillip's success at fishing is probably what gives him the courage to try his next accomplishment. Near the end of the chapter, Phillip gets up the courage to try and climb the coconut tree to harvest some coconuts. He is successful, and he and Timothy enjoy the well-earned nourishment together.
These things are vital for Phillip to learn because Timothy knows that he might not always be around to take care of and provide for Phillip. Readers are reminded of this detail at the beginning of the chapter. Phillip tells readers that Timothy believed that they might never get off of the island. Readers know that Timothy is much older than Phillip, so he won't always be around for Phillip. Phillip absolutely needs to learn to survive on his own despite being blind, and Phillip is coming to realize this fact. That is why he tells readers at the end of the chapter that he felt like he had graduated from survival school.

It was almost as if I'd graduated from the survival course that Timothy had been putting me through since we had landed on the cay.