It was Caiaphas and the Sanhedrin who found Christ guilty. Per the story the young rabbi challenged the Jewish elites teaching and practices, thus the high priests demanded he be put to death. Pilate obliged with some reluctance.
Rabbinical Judaism today is very different temple-centric Judaism practiced in Christs world. It was not until 70 AD was Titus razed the temple that rabbinical Judaism arose out of necessity. You really need to understand the Temple and how it was the center of ancient Judaism to grasp the story.
That is important to remember because it brings the argument to your first point. As temple-centric Judaism was all about the sacrifice, Jesus indeed did HAVE to be crucified. In a nutshell, the sacrifice of the Christ was the end of Judaism. No more sacrifices were required because the perfect one had been made, this anything beyond that was unnecessary perhaps even a blasphemy.
This is where you will see the Orthodox (Catholic, Coptic, Orthodox) different from Protestant teachings. They put a huge emphasis on the sacrifice itself, not just the Resurrection. Its also why the mass is called a sacrifice. Its also why Orthodox Christians have a corpa on the crucifix and Protestants never do.
On Edit: Catholic anti-Semitic behavior has historically been a disgrace