I resigned. Can I ask for a copy of the noncompete and is the employer obligated to give it to me? What about the 2 weeks? Am I obligated to fulfill the 2 weeks or can I not go to the office after giving my letter of resignation?

If you gave two weeks notice, you are still employed. Continue to go to work as you did before. It's your employer who may wish to terminate you earlier; if they don't say, assume you are still employed.

Ask for a copy of the non-compete. If they refuse, tell them that in that case you are not bound by it.