Theists: How can predetermined fate and free will coexist?

[Tonus]

If God weakly actualizing the circumstances to have Judas freely betray Jesus, that is not the same as God causing someone to do evil. While the effect was willed by God, the mechanism (Judas) still had free will. If God knew Judas was not greedy and selfish enough, then someone else would have been put in those circumstances.

That was just one of the possibilities that I was thinking through. I am assuming that it was of critical importance that Judas fulfill his role once it was prophesied. There is another option in the end-- that Judas is in heaven, having carried out his role in assuring that Jesus did not make a mistaken prediction. That's not the impression we get because Judas is used by Satan and he is allowed to suffer from a guilty conscience that drives him to suicide. There is no indication that he is redeemed.

There are other issues with the concept of a predetermined fate in this situation. If God foresaw that Judas would betray Jesus, then this means that God foresaw himself selecting Judas for the role. Is God also beholden to fate and unable to change the future? If not, then didn't his action in choosing Judas seal that man's fate as the person who betrayed God himself? That's a heavy burden to place on a man unnecessarily, since his betrayal wasn't needed-- Jesus himself mentioned that the Pharisees had plenty of opportunities to apprehend him, as he was not hiding.