Which part of the brain plays a major role in homeostasis by regulating such processes as heart rate and breathing through the autonomatic nervous system?

There are few cells in the body that do not undergo mitosis: most somatic cells divide regularly, some more than others. take for example the cells that line the digestive tract. these cells must be frequently replaced because they are constantly eroded by the movement of food through the tract. what mechanism(s) is/are in place to ensure that these cells are exact copies of the mother cell