I don't know why you think having free will means being unpredictable. One can be unpredictable, but that couldn't happen too frequently, because not all the time there are circumstances that would allow that. To illustrate, here's an example of an action, that most people couldn't predict:
https://www.youtube.com/watch?v=Ql9GL8bJ32Y#t=884
Yet it can still be expected by some, that already have experienced that. And with enough experience, those can probably even be predicted.
The problem is, we will never know, because there can not be a computer or a machine that accounts for
everything. You can be improving it by adding new features to it, that let it consider new facts, but you don't know all the facts either! Instead of making an omni-aware machine, you at some point will say: "Uh, I'm tired of doing this for 50 years.Let it burn already."
About decisions themselves. Elsewhere I said that decisions are always based on something. In the example above it's based on trusting such an impulse and knowing no disadvantages of trusting it. Or ignoring such disadvantages. If it's some good impulse, then it still matters how hard the choice is. But yes, any choice relies on something, be it physical reality or one's beliefs. But it also depends on priorities. Which might depend on literally everything in one's life, consciously or subconsciously. And so, you can't predict one's decisions perfectly, because there's no way to know all priorities of a man.
Now what if there was such an ability - ability to build an omni-aware machine? I think it would be able to predict everything. Would it mean people will stop having free will to choose? I don't think so. Interestingly, priorities are not exactly what
forces one to make a decision, but rather stimulate him: depending on your decision, factors that you consider important will be satisfied, which in most cases leads to you yourself also being satisfied. That might lead to someone else being abused though, so morality is another aspect that's involved. Note: a decision to ignore other's morality principles in order to satisfy his own priorities is a moral decision anyway.
I don't think it answers any of your questions, but my idea is that the world is absolutely complex, so there's no way to check if free will physically exists or not.
