Jesus and Herod

How did Herod react to Jesus?
Luke 23:8-12  8 Now when Herod saw Jesus, he was exceedingly glad; for he had desired for a long time to see Him, because he had heard many things about Him, and he hoped to see some miracle done by Him. 9 Then he questioned Him with many words, but He answered him nothing. 10 And the chief priests and scribes stood and vehemently accused Him. 11 Then Herod, with his men of war, treated Him with contempt and mocked Him, arrayed Him in a gorgeous robe, and sent Him back to Pilate. 12 That very day Pilate and Herod became friends with each other, for previously they had been at enmity with each other.”

Why did Jesus ignore Herod?
Jesus didn’t want to stoop to Herod's circus, and Herod didn't have the power to crucify Him.

Why did Herod send Jesus back to Pilate "arrayed in a gorgeous robe" (Luke 23:11)?
He was acknowledging Jesus to be a king, in jest, which Pilate appears to have appreciated: "That very day Pilate and Herod became friends with each other" (Luke 23:12).

What did Pilate do next?
Luke 23:13-16  13 Then Pilate, when he had called together the chief priests, the rulers, and the people, 14 said to them, “You have brought this Man to me, as one who misleads the people. And indeed, having examined Him in your presence, I have found no fault in this Man concerning those things of which you accuse Him; 15 no, neither did Herod, for I sent you back to him; and indeed nothing deserving of death has been done by Him. 16 I will therefore chastise Him and release Him.”

What is wrong with Pilate’s statement in Luke 23:14-16?
If he found “no fault” in Jesus, he should just release Him, not "chastise him" and then "release him."

Why did Pilate volunteer to "chastise" Jesus?
Most probably to try to appease the Jews enough to make them go away with something short of what they wanted: the crucifixion of Jesus.