Praetorium

What and where is "Praetorium"?
Derived from Praetor, a Latin word that means, "Leader," Praetorium is wherever the Roman emperor or governor, who represents the emperor, is staying or headquartered, whether it be his official residence or battlefield tent. The official residence of the Roman governor of Judea was at the port city of Caesarea, so that residence typically served as his Praetorium. When he was in Jerusalem to keep an eye on the rebellious Jews during their feasts, he stayed with the Roman garrison at Antonia Fortress, located adjacent to the northwest corner of the temple area and referred to as "Praetorium" above.

Why didn’t they want to go inside the Praetorium?
"Lest they should be defiled, but that they might eat the Passover” (John 18:17). Jews who entered a gentile's house, where there was leavened bread, during the Passover were considered "defiled" (John 18:28) and excluded from the celebration meals.

Who is "Pilate" (John 18:29)?
See Pontius Pilate.

Why did he have to go "out to them" (John 18:29)?
They wouldn't come inside, so he had to go out to Antonia Fortress' gate, where there were.

What is the Jews' initial response to Pilate's opening question?
"If He were not an evildoer, we would not have delivered Him up to you" (John 18:30).

Why do they respond in such vague terms?
Either they thought calling Jesus an "evildoer" would be good enough for Pilate to sentence Him to death, or something else is in play.

Who had gone to arrest Jesus a few hours earlier?
Six hundred Roman soldiers (see Judas Iscariot), among others.

Who must have approved the deployment of ten percent of his legion?
Pilate.

To win that approval, what must the Jews already have done?
Accused Jesus before Pilate.

Then why did Pilate ask them, "What accusation do you bring against this Man" (John 18:29)?
He is holding court and wants them to formally file charges against the accused.

What does the response of the Jews - "If he were not an evildoer, we would not have delivered Him up to you" (John 18:30) - amount to?
'We got the guy, so let's get this over with.'