Yes it does, that is why the Founders Grandfathered themselves in for NBC status.
Also see: "However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries."http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html
Bammie is not an NBC.
Yes [the Constitution recognizes a "dual citizen" category]
Quote the part of the Constitution that addresses dual citizenship, please.