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.

Falling from less than a metre think still generally ok but not too frequent. Playing and falling is normal and just be conscious of the possible bruises and watch out for any suspicious bumps or oddness in baby's behaviour after fall. Otherwise, should be fine. My girl fell when she was 4 months off my one metre high bed plus platform and scared the day lights out of my Wife.