Depends on the airline. SWA allows two carryons in addition to checked bags.
Yes, the laptop is allowed, and no, the xray will not hurt it. It did not harm our laptop, digital camera, digital camera compact flash or batteries. Warning: put the batteries for any camera in your checked bags. They look like bullets to the xray machine and they will search your stuff. We had our laptop carrier (it holds the laptop, camera and accessories) searched and "dusted" in BWI. Not a big problem, just time consuming.