Did Jesus give up his Jewish faith to become a Christian?
The only evidence we have is the text of the Gospels. The teachings of Jesus recorded there are within the range of teachings you'd find within the Pharisees, so if the only text we had was the Gospels, without Acts, Paul's letters and so on, scholars would probably conclude that Jesus was a Pharisee. Leaders among the Pharisees had desciples, Jesus had desciples. Jesus hung out in synagogues and argued with Pharisees, and typical Pharisees out in synagogues and argue with each other. The arguments got quite heated, more heated even than some of the Gospel quotations about the Pharisees. So, I'd say that there's no evidence that Jesus "gave up his Jewish faith."