Why do you think John included chapter 21 after his climatic statement about believing in Jesus as the Son of God? Chapter 21 doesn’t seem to support that main theme that well. (??)

Peter and Jesus use 2 different Greek words to talk about love in a word play that isn’t apparent in English.  For example, Jesus first asks Peter if he agape’s Jesus. Peter responds that he phileo’s Jesus. (Note: NIV does a bit better job than KJV at conveying the nuances of the Greek e.g. “do you truly love me”.)  It’s pretty hard to understand why Jesus asked the same question 3 times if you don’t have some sense of which words were being used.

Here is a pretty good article from BibleGateway.com that helps answer both questions (be advised that it is lengthy).