Does God have a predetermined plan for each individual? If so, how does with affect our free will?
God definitely has a plan for us. However, it is not specified to the level of detail your question seem to imply.
1 God, infinitely perfect and blessed in himself, in a plan of sheer goodness freely created man to make him share in his own blessed life. For this reason, at every time and in every place, God draws close to man. He calls man to seek him, to know him, to love him with all his strength. He calls together all men, scattered and divided by sin, into the unity of his family, the Church. To accomplish this, when the fullness of time had come, God sent his Son as Redeemer and Savior. In his Son and through him, he invites men to become, in the Holy Spirit, his adopted children and thus heirs of his blessed life.
This plan is an invitation. We are totally free to accept or reject this invitation. Our free will is intact.
So God does not have a strict and definite plan for each individual, rather he has a hope or will for us and we can freely decide to reject his plan and act contrary to his will?
Depends on what you mean by strict and definite? He is pretty strict on what is, or isn’t sin.
He gives us a variety of gifts. These gifts, talents, serve some pursuits better than others.
My belief is that God has a plan for each one of us. He calls each of us to a particular career and a particular vocation, as well as particular choices. However, we have the ability to determine whether or not we will accept that plan. If we do, it is the surest and most direct route to heaven. This has been demonstrated time and again by the saints. They had choices - but many of them listened to the Will of God and made their choice according to His Will.
This from the Catechism may be helpful:
Providence and secondary causes
306 God is the sovereign master of his plan. But to carry it out he also makes use of his creatures’ cooperation. This use is not a sign of weakness, but rather a token of almighty God’s greatness and goodness. For God grants his creatures not only their existence, but also the dignity of acting on their own, of being causes and principles for each other, and thus of cooperating in the accomplishment of his plan.
If you wish, read the whole section, 302-314, “God Carries out His Plan: Divine Providence,” which includes subsections “Providence and secondary causes” and “Providence and the scandal of evil.”
I wonder this a lot too. My idea is, God has a plan for us, but if we take a wrong turn, He has some sort of back-up plan. For example, if a teenager takes a wrong turn and gets pregnant, the back-up plan would be her baby. If she takes another wrong turn and aborts the baby, the back-up plan would be she has learned from her mistakes and will make better choices in the future (and so on and so forth). I doubt this is anywhere close to the correct answer, but I like to think of things this way–it helps me make sense of all the chaos in this world.