One last clarification, I believe God is omnopotent, omnipresent and all knowing. That being said he already knows who will choose to accept his free gift and who will not. He knew this before they were born if they would choose to be saved.
Yes, God "knows"--not merely because he knows all things, including the future. Rather, he knows because he is the one who makes it happen. Just as I "know" that I am going to have a cup of coffee in about 5 minutes, because once I've finished writing this paragraph, I'm going up to the kitchen to make it.
"When the Gentiles heard this, they began rejoicing and glorifying the word of the Lord, and as many as were appointed to eternal life believed" (Acts 13:48). Note: not "as many as believed were appointed to eternal life." The Pisidians did nothing to elect themselves. God did the appointing.
"he chose us in him before the foundation of the world" (Eph. 1:4) and also, "though they [Esau and Jacob] were not yet born and had done nothing either good or bad--in order that God's purpose of election might continue, not because of works but because of him who calls--she was told, 'The older will serve the younger.'" The point of saying "before the foundation of the world" or "were not yet born" is simply to say, salvation had to do with God's free choice, not theirs, because they did not exist.
What you are saying is first one must be the elect (chosen) to be saved and they must also choose to accept God invitation to be saved.
Please do not tell me what I am saying, especially if you're going to tell me what I am
not saying.
God chooses his people. They do not choose themselves. Israel did not choose to be the chosen nation. God chose them (Deut. 7:6-7). And Israel is a type of the church, so Jesus says to his disciples, "You did not choose me, but I chose you" (John 15:16). Those whom God chooses are saved, not against their wills, but willingly, because takes away their hostility and makes them willing: "I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. And I will put my Spirit within you,
and cause you to walk in my statutes and be careful to obey my rules" (Ezek. 36:26-27).
If they are not the elect then their hearts will be closed to the gospel and the Holy Spirit and will not desire salvation? Is this correct?
If they are not the elect, then they are God's enemy. "The mind that is set on the flesh is hostile to God, for it does not submit to God's law; indeed, it cannot" (Romans 8:7). Why would God's enemy want to please him?
Romans 10 implies it is up to us to share the gospel to the world?
Yes.
I quoted that passage from Romans 10 first, in fact, and you've already responded to that post. You don't seem to be paying very close attention.