Porcius Festus

Was Paul trying to flatter Festus by calling him "most excellent Festus" (Acts 26:25)?
κρατιστε (kratiste), the original Greek word translated "most excellent," was an honorific title used to address a high government official, which Festus was. We do likewise today when we address an ambassador as "Your Excellency" or a judge as "Your Honor." κρατιστε (kratiste) also can be translated, "most noble," and to an extent Festus fit that description better than his predecessor Antonius Felix or his successor, as history records Festus' governorship as relatively fair and benevolent.

Then why did Festus cry out as he did?
Festus was still an unsaved sinner, and Paul's "defense" (Acts 26:24) may have disturbed Festus' sin nature enough that he felt ill at ease; Festus sounds like he may be trying to brush aside Paul's testimony and message about the "forgiveness of sins" (Acts 26:18).

Does Paul let Festus brush him and his message aside?
He stands his ground - "I am not mad ... but speak the words of truth and reason" (Acts 26:25) - and then pivots from Festus to Agrippa (see below).

Why does Paul ask Agrippa if he believes "the prophets" (Acts 26:27)?
He is asking if Agrippa believes what the Old Testament prophets said about the Messiah, or more precisely if he believes that Jesus is the "Christ" (Acts 26:23) prophesied by those prophets.

Was Agrippa being serious or sarcastic when he said to Paul, "You almost persuade me to become a Christian" (Acts 26:28)?
The context indicates him to have been serious, for three reasons. First, Paul observed, "I know that you do believe" (Acts 26:27). Second, there is no sarcasm or ridiculing of Paul when Agrippa, Festus, Bernice and others discuss him among themselves. Third, Agrippa "stood up ... and ... [went] aside" (Acts 26:30-31), followed by "those who sat with" (Acts 26:31) him.

How does Agrippa standing up and going aside indicate that he had been serious and not sarcastic?
When the judges at a trial wanted to have a discussion without the accused listening, it was invariably the accused who was put "outside for a little while" (Acts 5:34, see Gamaliel), not the judges who got up and moved. And these weren't average judges. Agrippa was a king, who, having entered the auditorium "with great pomp" (Acts 25:23), was sitting not on the floor but on a throne or a throne-like chair, and his sister Bernice and Festus, the Roman governor, would have had seats of equal prestige. It was unheard of for a king, a Roman governor, and their counselors to yield an auditorium packed "with the commanders and the prominent men of the city" (Acts 25:23) to a prisoner in chains, while they went off to a corner for a huddle.

Then why did Agrippa suddenly stand up and go aside when Paul said to him, "King Agrippa, do you believe the prophets? I know that you do believe” (Acts 26:27)?
The same reason some people squirm and leave their seats today when asked after hearing the Gospel if they believe: their seat suddenly gets too hot for them.

Whom else did Paul tell should become a Christian?
Everyone in the auditorium: "I would to God that not only you, but also all who hear me today, might become both almost and altogether such as I am ..." (Acts 26:29).

What was Agrippa's verdict?
Paul neither deserved the death penalty nor was even a criminal: "This man is doing nothing deserving of death or chains" (Acts 26:31).

What could have happened if Paul hadn't appealed to Caesar?
"This man might have been set free if he had not appealed to Caesar" (Acts 26:32).

Had Paul made an error by appealing to be judged by Caesar?
Had Paul been released, the Roman guards would no longer have protected him against Jewish assassins and he also would have lost his Roman guard-escorted, all expenses-paid voyage to Rome, which is where the Lord wanted him to go. True freedom isn't physical but being at the center of God's will for our lives, even if that means physical chains.