I was always worried when they were very small that I would break them or hurt them in some manner, they come out so small. After each kid that fear diminishes a little each time but never goes away.
I don't think the fear of doing it wrong ever goes away but as you watch them grow and see them turn into little thinking, speaking and exploring children you can see your influence.
At the ages you speak of as long as you are providing them with life's needs and spending time with them, you're an amazing father. The bonding also seems to come easier the more direct care you do the younger they are. Feeding, changing, rocking, bathing and so on. Many mothers take on this role 80% of the time while dad does about 20% so mom's normally bond faster as they have been since they were still growing the baby. Men will never experience that, a baby is growing inside of me. That is a disadvantage to bonding, it has nothing to do with you being a bad father. You're just given a child at a disadvantage to their mother.

I completely agree about C-Sections. It looks like a bad gore film. Big hole, guts flipped all over in what seems like a sloppy mess. I've done it all as far as birth goes and I am honestly best with the C-Section. Other than worry for my wife I don't mind the guts and blood.

Now go make another one, 3 isn't a test to your defense at all.