Carol,
"You said, "high priests (the Sanhedrin)"
Jewish

"Was there any sort of law that he was being arrested for? How was he threatening the Temple, public security, or the Roman Empire?"
It was Passover and Jeruslem was very crowed. He was threatening the entire Jewish Preistly Heirarchy and the Roman Empire by being a traitor to Judaism and a rabble rouser for the Romans.

"In whose eyes, or according to whose standards of criminality was it considered a crime to kill Jesus, and why would Pilate want to wash his hands of it?"
Because he was semi popular with the unwashed masses, nobody wanted to take the responsibility for killing him, hence the buck passing, just like all beauracrcys everywhere.

"One other question: are the Gospels the only historical accounts of these events? Did any mention of these events show up in any historical accounts kept by the Romans, Jews, or anyone else?"
Not sure, but I think some of it does show up in Roman stuff, will find out about the Jewish stuff, but I think it shows up there. Judasim admits he exists, but not that he was the Messiah. Islam also recognizes him as a prophet.