You asked

What are the benefits of breastfeeding?

Breastfeeding is the one thing that a mother can do to help her child in future life as far as sickness and disease are concerned. It is the most natural and beneficial act that a mother can do for her child. Studies have shown that tremendous benefits pass from mother to child through breast milk - from the antibodies that protect the new baby at birth, to the special nutrients that protect the baby from certain childhood diseases. Absolutely nothing can duplicate the properties of breast milk. It is nature’s way of ensuring the health and quality of life for your baby. Also, a very special bond is developed between mother and child during breastfeeding.
Just some of the benefits of breastfeeding for babies include the fact that they get the most complete and highest mix of both nutrients and antibodies. As your baby grows, she has different nutritional needs - breast milk changes and keeps pace with your baby’s growth. Unlike milk formula, breast milk does not cause vomiting and diarrhea in children. It reduces the risk of colic, chronic constipation and other stomach upsets and also reduces the risk of childhood diabetes.
It gives protection against ear infections, pneumonia, kidney infections, and scepticemia. Breast fed babies are also far less likely to suffer from allergies, asthma and eczema. The risk of sudden infant death syndrome is also reduced drastically in breastfed babies. There is also a reduced risk of tooth decay as well as heart disease later in life. Antibody response to vaccines is higher and there is also a reduced risk of childhood obesity. These are just a few of the benefits to babies who are breastfed - there are many, many, more.
Mothers too, benefit greatly from breastfeeding. They are less likely to develop ovarian, breast, cervical, and endometrial cancers and a reduced risk of anemia. They are also less likely to suffer from osteoporosis later in life. One great benefit to breastfeeding is that it helps mothers reduce excess weight after giving birth and also helps the body to return to its pre-pregnancy state a lot faster. Mothers who breastfeed save a lot of money as well. Breast milk is free, and breastfed children become ill less often, thus reducing the costs of medical bills. 
These are just a few of the numerous benefits to mothers who breastfeed their babies.

More questions

Concern over give infants cold medicine
Firstly, you need to determine if it is vomiting or if they are just possetting, bringing up small quantities of milk. 
Colic is the medical term used to define excessive and frequent crying in an otherwise healthy infant that lasts for more than three hours a day for more than three days a week for at least a period of three weeks.
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Colic won’t harm your baby in any way and most babies outgrow it by the time they are between three months and four months old.
It is recommended that you seek advice from your GP when the colic or persistent crying begins. 
The persistent nature of colic means that there are likely to be times when your baby cries, whatever you do.
Cradle cap (seborrhoeic dermatitis) is a rash that starts as scaling and redness on a baby’s scalp.