Newport News Shipbuilding has built all of the Nimitz class carriers and will build all of the Ford class carriers. It has never been a government run shipyard; it has been a private business since it's inception. It has had several owners over the 100 or so years it's been around, including Northrop Grumman.
No government yard currently builds CVNs, but they do perform maintenance and overhauls. Refueling is only performed at NNS.
Carriers are designed to hog and sag somewhat with sea loads just like any other ship. Ships are not "hinged."