Sure they can. Google, Apple, Oracle, the Apache Software Foundation, GNU, Linus Torvalds, Amazon, and the linux community all compete against Microsoft. They are winning too. Microsoft has been driven completely out of the phone market, the automotive market, and most of the server market. They are currently in very serious trouble with the desktop market.
Illegal, and unsuccessful. The federal government has no authority to break up Microsoft or any other company. Nothing in the Constitution gives them that authority.