John F. Kennedy International Airport’s Terminal 8 will undergo a $344 million overhaul as part of a $13 billion redevelopment of New York City’s main international gateway. The plans, announced Wednesday, solve a piece of a complex puzzle in which the Port Authority of New York and New Jersey, which runs the airport, seeks to redevelop the busy hub while keeping it in operation … The redevelopment plans envisage $12 billion of private investment matched by $1 billion in Port Authority funds.