Hello,,, is your baby able to sit,? And is your baby able to stand with support? His your baby recognises his mother or you? Is your baby feeding well? If yes to all these then no need to worry, your baby is growing normally as other children. At one year, baby should have 3 times of his birth weight (if 2.5kg at birth then at one year baby should be atleast 7.5kg) if so then your baby is gaining weight normally. Fast growing of hair and nail is pretty common in some babies (due to genetic issues) and it is not a problem (if your baby doesn't have any congenital anomalies) and all babies always try to resist cutting of hair or nail because babies don't understand it,,(so become afraid) and it always irritates them. So don't worry sir,, if you still have doubts, get back to me with answers for above questions and with birth weight and current weight of your baby.