Whether it is correct to strictly adhere to the regime or give the breast on demand?

Unequivocally: breastfeeding should be on demand. There is no need to fear that the baby will have too much breast milk. Let the baby eat as much as it wants. The more often the baby sucks a breast, the better it will gain weight and the stronger will be its immunity. When a child gets enough of milk, it throws the breast itself.