A. No, it doesn’t. That’s why it says “the right of the people to keep and bear arms shall not be infringed.”
B. The legal definition of “the militia” under U.S. Code (10 U.S.C. § 246) is:
“The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States; and of female citizens who are members of the National Guard.”
So, in context, the “militia” literally includes most adult citizens, not just the National Guard.