Did Jesus know that Judas would betray him, and why didn't he try to stop Judas?

Jesus did stop the betrayal.

The betrayal was a betrayal only because the motivation for it was diabolical.

When the last day arrived, and not until the last day arrived, Jesus cast the prince of this world out of Judas, pursuant to the will of his Father. That cleansing act left Judas with no desire to fulfill his obligation under the covenant he made. Jesus aborted the betrayal.

After Judas was thus raised up again, Jesus put it into his heart to fulfill his obligation under the covenant. That motivation for fulfilling his obligation was not diabolical.

Instead, Jesus set the stage for his words to be fulfilled: If they have called the master of the house Beelzebub, how much more shall they call them of his household.