Secondly regarding the question of who people say Jesus is it seems that the fact that Jesus is asking this question must have a reason. Other passages in the Gospel show clearly that Jesus has divine knowledge of people's thought, so surely He already knows.
But putting the two together it is possible to see a model of how we dialogue with God and how this encounter affects our lives and through us the lives of others. It is from his inward conversation with God that Jesus' question of who people say He is flows. An opportunity is given as the disciples approach Him to engage with Him. The moment of prayer and contemplation flows into a moment of an opportunity and of action of a deeper encounter. We can see that it leads to a deeper understanding, as Jesus now gently guides His disciples to the teaching which follows, the teaching that "the Son of man must suffer many things, and be rejected by the elders and chief priests and scribes, and be killed, and on the third day be raised." (Luke 9:22 RSV) Following Him will mean the same for His listeners then as for us now: "If any man would come after me, let him deny himself and take up his cross daily and follow me." (Luke 9:23 RSV)
Another aspect is that Jesus is also asking us every day who do we say He is. Do we answer with St. Peter "The Christ of God." (Luke 9:20 RSV)? Or is the answer maybe not as complete and do we see Jesus as a good teacher, a prophet or maybe even just a good example? But it is a question that is asked daily of us, a question on where Jesus is standing in our lives and which role He has to play. It seems that it is important to at least try to give the right answer and realise that Jesus is our Lord and our God and allow Him to take that role. As this Gospel illustrates, it is through prayer, through the sacraments, and also through others that we come to encounter Jesus. In these ways we hear His voice asking us the question what He means to us. Jesus is not asking because He is looking for the answer, but because He wants us to draw closer to Him.