The first part the only Roman who was a Jew was I think Paul. He was half Jew. The Romans were never Jewish and didn't follow Jewish laws. They were the "government" authority of Rome. The Jews found fault in Jesus and turned him over to the Roman authority (the government/govenor) to be crucified. You are right, the second part. My correction it was Pontius Pilate rather than Harold who didn't want to crucify Jesus but did anyway from the pressure of the Jews to do so.
Pontius Pilate, Latin Pontius Pilatus (died c. 36 ce) Roman prefect (governor) of Judaea (26–36 ce) under the emperor Tiberius who presided at the trial of Jesus and gave the order for his crucifixion.Jun 1, 2015
Britanica Encyclopedia and
and "Pontius Pilate, Latin Pontius Pilatus (died c. 36 ce)
Roman prefect (governor) of Judaea (26–36 ce) under the emperor Tiberius who presided at the trial of Jesus and gave the order for his crucifixion."
Britanica Encyclopedia
42. Jesus Before Pilate: Part I (John 18:28-38)
The second part, yes, the Jews pushed the issue. The Pontius Pilate gave Jesus to the Jews because he say no fault in his claim or statement.
The only person "on Jesus side" who is Roman is Paul because of Roman citizenship as according to Acts 22:22-23:11.
"The commander went to Paul and asked, “Tell me, are you a Roman citizen?”
“Yes, I am,” he answered.
28 Then the commander said, “I had to pay a lot of money for my citizenship.”
Does it make a difference, though?