Moses, peace be upon him, performed a miracle, by God's permission, when he and his followers reached the sea followed by Pharaoh and his soldiers. God commanded water to change its physical laws so the Israelites could get safe to the other side. That was a miracle, something real taking place opposing the natural physical laws. As for magic, it's an illusion, it's not real.
What Jesus, peace be upon him, performed by God's permission, were miracles. Speaking in the cradle a few hours after being born to deffend his mother and announce who he was, is not magic: it's a clear miracle. So were all the other miracles he performed, which are recorded in the Qur'an
2- The Jews at the time who followed him were following God's Messenger. Whether they knew him as Messiah or not was not the point. The point is Jesus was God's Prophet and Messenger, and believers since the time of Noah are commanded to follow the latest Prophet sent by God, in this case Jesus, peace be upon him
I'm speaking from a Muslim perspective, as we believe that the message of Jesus supercedes that of Moses, and that the final revelation from God to Prophet Muhammad, peace be upon him, supercedes all previous Divine Scriptures ...