No. Although the names are somewhat similar, polycystic ovary syndrome and polycystic kidney disease are completely different. Polycystic ovary syndrome is not related to and is not a cause of polycystic kidneys, and polycystic kidney disease is not related to and is not a cause of polycystic ovary syndrome.
No-they're different. Adult-onset polycystic kidney disease is a genetic disease that passes directly from one generation to the next (autosomal dominant). While cysts may be found in other organs such as the liver, the ovary is not one of them. Polycystic ovary syndrome is not generally inherited directly (can run in clusters like many other diseases) with the roots of the disease involving male hormones and insulin.
No you do not. Theree is no corelation between the two.