Pelagius (allegedly) claimed man doesn't need the grace of Restoration (Baptism) in order to be free to choose. The Church never taught that, which is why Pelagianism is heresy, by definition.
And, as [stafassisi] stated, it is God's will for all to be saved
Yes, that's biblical.
God shares His grace with all men
No, God offers His grace to all men. After Christ redeemed mankind, that became possible.
man needs to make a choice
That comes with freedom. God doesn't make our choices. That would make us robots.
God hates the sin that man produces so much so He has a Lake of Fire waiting to cast us into where the worms will torment us forever
The Bible tells us the lake of fire was created for the devil and his angels, not for mankind. The transgressions of angels are unpardonable. But for mankind, God offers salvation. That some men will end up in the Lake is because they chose to follow Satan and not God. It is their choice, not God's. God does not force us to sin.
God deliberately allow the fall of Adam, so I think it's rather difficult to say that He did not predestined it.
God did o such thing. He gave Adam and Eve freedom, wide freedom, save for one restriction, lest they have unlimited freedom and only God has that. "Man has to know his limitations." (good old Clint Eastwood!)
It is absolutely essential that man is free. If we were not free, then who would decide for us? If God made our choices, we would indeed be robots. But, being free, we can resist Satan. He has power over us if we allow him to have power over us, if we give in to his deception, if we let him convince us that God is a liar, the way he did Eve.
By choosing God and resisting evil, we can be moral beings. God wants us to be rational, merciful, moral beings.
By giving us freedom He also knows that some of us will (ab)use that freedom and loose it. That's what happened to our ancestral parents. But God did not abandon them. He did not send them to hell. He gave all mankind a chance to come back to God, to be restored to life. As stfassisi says, one must persist in that sin until the end in order to lose his life. The unrepentant soul goes to hell.
If God deliberately predestined Adam and Eve to fall from grace, then why was He saving them? Such a "God" is more a pagan, masochistic deity than the one True God we know in Christ.
He did know what their unfortunate choice would be, but He did not force them to sin. And, despite their transgression, He did not abandon them, or, for that matter, the whole world.
Why? So that we can tell Christ, "You did not choose us be we chose You?" That is, after all, what you are saying. But that is not how it works. Man is either a slave to sin or a slave to righteousness; it is an either/or type of deal. Only our Lord can make us a slave to righteousness.