Was William 2nd William the conquerer's son?

YES, William II (c. 1056 - 2 August 1100), was the third son of William the Conqueror (William I), and was King of England from 1087 until 1100, with powers over Normandy, and influence in Scotland. He was less successful in extending control into Wales. William is commonly known as William Rufus, perhaps because of his red-faced appearance, or red hair.