The answer to your first question is “yes”.
The Revolutionary War was fought, in the main, between British citizens, who, in 1775-1781—technically had the same king.
The Treaty of Paris in 1783 sorted that out quite nicely.
The War of 1812 was fought between actual nations, thus it was not a civil war. The British invaded America.
But, you knew that.
I disagree with you.
More importantly, Samuel Huntington, Roger Sherman, William Williams, Oliver Wolcott - all representing Connecticut - they disagree.
As does Thomas McKean, George Read, and Caesar Rodney - all representing Delaware - they disagree.
As does Button Gwinnett, Lyman Hall, and George Walton - all representing Georgia - they disagree.
And so forth and so on through the roll call.
Here is part of what they said: “When . . . it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which . . .”
Further, they said: “ . . . Governments are instituted among Men, deriving their just powers from the consent of the governed . . .”
Further, they said: “ . . . whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government . . .”
In conclusion they declared - “ . . . That these United Colonies are and of Right ought to be Free and Independent States: that they are absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved.”
Sometime before, but certainly no later that July 4, 1776,
the colonialists stopped being British citizens and no longer had a British King.
Of course, the King of England disagreed with all of this. And, apparently, so do you.