Is it true that wemon with pcos, after sucessfully giving birth to a child that the pcos will go away?

No. Pcos is an inherited disorder and will never go away. Symptoms and lifestyle problems related to pcos can change over time, and weight gain or loss often changes things. Pregnancy does nothing to alter the course of pcos longterm.
Not true usually. Usually go back to your prior condition, but anything can happen. The symptoms and problems of pcos shpould be able to be dealt with appropriately by your gyn or endocrinologist.