settlement fee is the same for an adult and a child but for FLR or ILR its roughly around half the cost of an adult, but then not long ago it was free when the child was included on the parents FLR/ILR app form.
almost certainly if the mothers (probably the mother is the one who's is applying 95% of the time) is refused the child's visa will be refused too, because the child is a dependent of the mother, basically what happens visa wise to the mother, will probably happen to the child.
more likely to happen is the mother will be granted and the child refused because the mother hasn't proven 'sole responsibility' or custody of the child.