“Free” is free from coercion. Man is not impeded to exercise his will for the choices available to him. An example I give is a man capable of an act of charity or an act of selfishness and chooseing either one and not the other. Another example I give is a chess player capable to make one move or another and make one and not the other.
“Foreknowledge of God” is the divine knowledge of acts (or generally any events) that the human actor has not committed yet; that is, God knows the choices ultimately taken by man before the man even considered them. It is important to understand that God exists outside of time and therefore terms like “fore” (meaning “prior”), or “after” do not apply to God’s knowledge, but rather to our knowledge. It can be likened to an exceptionally good chess player knowing the game and his partner so well that he always knows what moves his partner will choose to make. It also can be likened to an observer standing on top of the mountain who can see the road ahead of the traveler, and the strength of the traveler, and is therefore capable of knowing whether the traveler can reach the destination before the traveler even begins his journey.
The scripture gives numerous examples of people exercising their free will and of God foreknowing what they will do. First, the Gospel and the epistles contain multiple exhortations to virtue — every epistle of St.Paul, for example, devotes the concluding chapters to such inspiratonal advice. It would make no sense to ask people to act in a moral way if they had no way of choosing their acts. The one prayer Christ expressly asked us to pray contains the plea that God’s will be done on earth, as well as expresses the fear of temptation, both indicating that asides of the will of God there exists a free will of man. Jesus foreknows the betrayal of Judas, and His passion, the cowardice of St. Peter, and the martyrdom of saints.
One strong prooftext for predestination of the reprobates (which theory the Church does not endorse) is the passage in Romans where man is likened to clay that God shapes like a potter. However, that merely shows that sovereign God makes both a virtuous man and a sinner; it certainly does not say that God intends to specifically make sinners any more than a potter would intentionally make broken pots. So that is prooftext for sovereignty of God but not for absence of free will.
In order to adequately address the many concepts you have presented here, allow me to take just one at a time and probe a little further. I will eventually get to all of the matters.
First, “Free” you tell us, means “free from coercion”. I gather from your context, and the ordinary understanding of the word, coercion is “forced compliance.” Compulsion, oppression, bullying. In other words, I would be coerced into choosing green sox if I really wanted to choose blue sox, but noticed my hand being forced over to the other side of the drawer toward the green sox. Try as I might to make the other selection, somehow, perhaps mystically, my hand is pushed by an unseen force over and then, as if by magic, my fingers are pried open and my hand pressed down. Acting just like the arcade game where the crane claw closes upon the teddy bear I don’t want, my hand closes upon the green sox and I pull them from the drawer. All the time, my brain is screaming, “Don’t take them; drop them and pick up the blue pair.” But, without sufficient power to overturn the choice, I take them and put them on.
If I get the picture right, this to you would be coercion and you would not consider it “free” choice of sox. These are not trick quesitons or remarks. I really don’t want to put words in your mouth, so I am attempting to get your concepts clearly understood. Do I have this concept of “free” correct?