“A similar case can be made for the American Revolution as being a civil war.”
The Revolutionary War was America’s first civil war?
Would that make the War of 1812 America’s second civil war?
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.