In particular for capital punishment in Jerusalem during the time of Pontius Pilate. I'm curious about the account of events viewed as a legal proceeding.
Did the Jewish leadership really need Roman authority to execute someone? Could the Jews even arrest anyone of their own authority in Roman occupied Jerusalem or did they have to course those things through the Roman authorities?
Would a pardon such as Barabas received be granted that capriciously?
Would Jesus have been entitled to legal counsel? Was there a particular prescribed form to the trial?
Was the manner in which the conviction and the death sentence was arrived at in keeping with Roman law?
Was the crime for which Jesus was convicted that of insurrection against the Roman empire? Was there a particular law or statute that would have been invoked?
Was death by crucifixion the correct legal penalty under the law?
Would Roman soldiers really speed crucifixions along by thinking to stab the convict dead?
Is there anything implausible to detailing guards to the deceased's tomb?
Would a pardon such as Barabas received be granted that capriciously?
According to The Trial and Death of Jesus by Haim Cohn, the nighttime Sanhedrin court and the release of Barabbas are "so unrealistic and unhistorical as to verge on the ridiculous".
Would Roman soldiers really speed crucifixions along by thinking to stab the convict dead?
It seems unlikely. The purpose of crucifixion was to give the condemned a long, humiliating death by exposure.
Was the crime for which Jesus was convicted that of insurrection against the Roman empire?
Treason was the main crime for which one could be crucified. As portrayed in the Gospels, that would be the likely charge against Jesus.
The Talmud (Sanhedrin 43) offers a tantalizingly different account in which Yeshu was hanged (by the Jews, not the Romans) on Passover on charges of sorcery.
It should also be kept in mind that Pilate was known for being cruel and corrupt. On numerous occasions, he slaughtered large numbers of people who threatened his authority and civil order. His reticence to convict Jesus in the Gospels is generally considered uncharacteristic of him.
I can't say anything to most of your questions, only a few. But before I start, keep in mind that the account in the Gospels isn't entirely the same.
The questions I have an answer for:
Was the manner in which the conviction and the death sentence was arrived at in keeping with Roman law?
According to Klaus Haacker (German Theologian), Roman law allows for immediate execution - without formal trial - in any of the following cases:
The crime was public fact (=the criminal was caught red handed).
The accused confesses.
The accused refrains from defending himself.
The "public anger" attests to the crime and demands immediate punishment.
Depending on the Gospel, several of these conditions are fulfilled.
I don't know how accurate this representation of Roman law is, to be honest. If it is true, then the conviction and death sentence was arrived at in keeping with the Roman law.
edit: I'm having trouble finding out which ancient source Haacker is basing this on, since I don't have direct access to his work right now. Take it with a grain of salt.