To get the child back the crocodile must do what the mother says, this eliminates the answer "you will eat him". Also if the mother says "you will give him back" that leaves the crocodile free to eat the child. To eat the child the crocodile must bite the child; however crocodile bites are not inherently deadly, thus the mother should say "you will bite my child" the crocodile will start to eat the child by biting him then be forced to give the child back.
The paradox states "the barber shaves everyone who does not shave himself/herself, but no one else.", this means that another barber canot shave him as he would then be one of the people not shaving himself and the barber in question can not shave himself as he can only shave people who do not shave themselves. This leaves one logical conclusion, the barber does not shave.