The 2nd Amendment is not about service in a militia. The 2nd Amendment is about the conditions that must exist for a militia to be possible, and that PRE-condition is a population of individuals who are already armed. Sort of hard to conceive a well regulated militia with individuals with Yo-Yos and Frisbees.
Correct, but not for the reasons you list. The Second Amendment is about the balance of power between the government and the citizens. The Founding Fathers knew that if the government had all the guns, the citizens would have no protection against an abusive and runaway central government.
Also, in the days of our nation's founding, militia's were comprised of citizen soldiers. During times of national emergencies, there would not be time for these citizens to go to a central armory to withdraw a weapon.