Is it ok to let baby to fall down for them to learn? Will it hurt their brain? As I don't wish my kids too protective also. My baby 8months now. I bought a thick carpet for her (2inch). She always unaware and fall behind while sitting.

Let baby practice using her muscles, especially on transitonal movements. For example, let baby try to stand up on her own instead of rushing over to support her up, as this will deprive her of the practice of those muscles involved. As for falling down, I will always have my safety hands behind for my baby to fall a bit; free fall only on mattresses. Falling behind while sitting is probably a development stage where she is not ready to sit upright yet and cannot control it, and it will be so sayang to let her just fall on the back of her head all the time. I will say be protective depending on situations, trust your motherly instincts. =)