The Roman centurion in Luke 7:3ff obviously had some connections: “The centurion heard of Jesus and sent some elders of the Jews to him, asking him to come and heal his servant. When they came to Jesus, they pleaded earnestly with him, ‘This man deserves to have you do this, because he loves our nation and has built our synagogue.’” Obviously, he was already committed to God and his faith in Jesus was only an extension of his faith in God.
How does 7:23 fit in with proof that Jesus is the one to come: “Blessed is anyone who does not stumble on account of me”?
There is such sweet irony in 7:39ff: When the Pharisee who had invited him saw this, he said to himself, “If this man were a prophet, he would know who is touching him and what kind of woman she is—that she is a sinner.” Jesus answered him, “Simon, I have something to tell you.” Simon said “to himself,” but evidently Jesus, being more than a prophet, heard him and answered knowing full well both who she was and how Simon felt about it.
Luke 9:20 is Peter’s answer to Jesus’ question about who they think he is. Luke does not make a big deal out of the answer. Luke does make something at 9:33 of Peter’s response to the transfiguration, nothing that “he did not know what he was saying.”
In order to understand 9:52f you need to know the animosity between Jews and Samaritans. This incident only reinforces the radical nature of Jesus speaking to the Samaritan woman at the well and the story of the good Samaritan which follows.