Baby baptism is not taught in the Bible. What is taught it complete submersion into water, which you obviously can't do with a baby. And baptism was always done with adults whom had decided to make a public expression of their faith. If someone does baptize their baby as an expression of their commitment to their child's upbringing in God's Word, that's fine. But the child should still be baptized later when he/she can make the decision to commit themselves.
As for predestination vs free will. Free will is not Biblical. It's something people have made up to make themselves feel like their are in control.
Romans 8:29-30
For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers.
And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.
Ephesians 1:5
he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will
Ephesians 1:11
In him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will,
While God knows and directs all things, we do not know what He has in store, which gives us the illusion of free will. Now this does not take away from our responsibility. Because while God created us as we are, we are who we are. And God would not make you do something that you wouldn't do assuming you did have free will.
As a illustration, imagine that God was a novelist and we were characters in His book. (This simile has already sort of been used in the Bible.) Imagine He creates an evil villain who wishes to take over the world and is willing to kill everyone who gets in his way. Now wouldn't it be against this characters' nature if he decided to help a small village which has experienced a fire to recover? Don't you think it would make more sense for the author to write that this villain takes advantage of the village's weakness?
Now God can and has changed peoples' natures before. Paul, for example, was a murderer of Christ followers, but God appeared and changed him into a great apostle. In this case, it was God's will to change Paul's nature.