Increased estrogen. Liver normally metabolizes estrogen. With cirrhosis, estrogen levels become elevated as liver cannot break it down. The production of prolactin is stimulated in the pituitary as a result of increased estrogen.
Several reasons. The etiology of this is not entirely clear, but it appears that cirrhosis interferes with normal brain Dopamine levels, and prolactin was once known as Dopamine inhibiting factor (before it was discovered to be a discrete hormone of its own and its structure figured out). In addition, the high levels of estrogen which occur because the liver doesn't metabolize it right also increases prolactin.