You don't waste time with easy questions, do you?
Do you believe that eternal life is given to us now? I ask this because of your example of the baby.
Yes. I believe that in eternity past God knew that mankind would sin, that He would provide a just path to redemption that anyone and everyone was capable of doing, and that no man or woman would actually choose to do what is required. (Romans 3:10-18)
I believe that the reality that no one would be saved if God left any part of it up to man was unacceptable to God, therefore, God chose to foreknow (fore love) some. The elect, his sheep. That for these people, eternal destiny is a matter of God's good purpose and eternal glory. So they have ETERNAL LIFE before they are born. Through no personal merit, but because God wills it so.
Do you believe God disallows believers to commit certain sins? I am very confused on this because you seem like you believe God does give us free will, but at the same time it may be "limited" free will?
All free will is limited. I desire to flap my arms and fly, but physics limits my choices to what is possible. Is a man a thief because he steals, or does a man steal because he is a thief? Who chooses of their free will to be mentally ill or suffer a drug addiction? Why don't people just exercise free will and quit smoking, or pornography? So absolute free will is already a myth.
A truth in life is that, by and large, people will be who they are. The person who overspends because buying stuff fills some emotional need and ends up in deep debt, if rescued from that debt, will immediately go back to the destructive behavior that they just pledged to never do again.
To answer your question directly, yes.
On the one hand, God is the only one that I have met who actually seems to be able to change human behavior. Only God can make the drunkard, sober. Can make the liar, honest. Can change the heart of the thief and make him want to work.
On the other hand, and directly relevant to the discussion on walking away from God, maybe you can. I have no power over anyone else and God does not consult with me, but I cannot. I do not state that as opinion, but as fact. I was there. I tried. I know EXACTLY how it feels to opose the will of God and exactly what it would have taken to walk away from my salvation. I was unable to do it. I wanted to. I was prepared to. God literally said "No." The first, last and only time I ever heard him. One syllable that knocked me off my feet.
So no scripture or logic argument can override my empirical evidence to the contrary. You may be able to lose your salvation, I have no idea, but I cannot lose mine.
Do you believe faith is needed after the new birth? If so, what purpose does faith serve in our life?
Yes. New birth is not a goal, it is more like a metamorphosis. A caterpillar enters a chrysalis and a butterfly emerges. Faith is the air beneath the wings that holds the butterfly aloft. We are a new creation. We have a new life. We serve a purpose ... not a new purpose, because before, we had no purpose but only a zombie-like existence as an animated corpse. Now we have a work to do, prearranged by God and designed perfectly to match our gifts and personality. What we do has eternal consequences because we are the whiskers on the brush that God is painting the canvas of His great plan. Why would anyone want to give up on being part of this? How could they?
Down to earth. Down to a practical level. Faith allows us to see the hand of God in the hard times. When one brother is murdered and a second commits suicide because he believes that the next life will be better than this one and he just can't bear the sadness any longer ... Faith allows me to believe that God is still good and that he still does things for a reason.
So that when James returns to church after falling into crack again and says "life is hard", I can say "I know, but God will get us through. We'll just huddle together and get through this."
I cannot imagine life without faith.
Arthur