Was it right on Pilate's part to allow Jesus to be crucified? Was he culpable?

20/20 human hindsight says “Of course Pilate should have listened to his wife.” But God’s ways are greater than ours, and who am I to question them?

Pilate knew Jesus was innocent and condemned Him to death anyway. That was wrong and he was culpable.

Does Pilate's desire to save Jesus, washing hands, people's pressure, etc change things in any way?

The Son of Man will be betrayed, but woe to him by whom he is betrayed, it would be better for such a one if he never been born. That statement refers not just to Judas, but I think, to Pilate as well, because while Pilate was not a friend of Jesus like Judas was, he still betrayed Jesus by condemning him to die even though he knew Jesus was innocent, that it is a kind of betrayal.

Yes, these things increase his guilt.

Can it be said that he tried and failed?

Or that he tried, failed, and gave in.

it's a moot point whether the High Priests or Pilate condemned Jesus.....it was all in God's plan..

Matthew 16:26

From that time on Jesus began to show His disciples that He must go to Jerusalem and suffer many things at the hands of the elders, chief priests, and scribes, and that He must be killed and on the third day be raised to life. 22Peter took Him aside and began to rebuke Him. “Far be it from You, Lord!” he said. “This shall never happen to You!” 23But Jesus turned and said to Peter, “Get behind Me, Satan! You are a stumbling block to Me. For you do not have in mind the things of God, but the things of men.”…

In one way yes, another no; "Therefor, those who handed Me over to you have the greater sin."