In other words, to what extent was the American Revolution a "brother-against-brother" civil war?
Depends what you mean by British soldier. If you mean one who fought as a Loyalist soldier then yes. I'm not 100% certain with Americans as British Regulars but the British Army did try to recruit in the South as their strategy to "Americanize" the war, which meant getting Americans to join them instead of only relying on soldiers sent from Britain.
I'm trying to go through my stack of notes to find which book it was that said this, but the British-born looked down on their American-born compatriots, even calling them barbarous. There was definitely a sense of hierarchy and condescending attitudes going around. Several British officers despised using militias from the colonies as many were undisciplined and often broke conduct such as looting houses and scouring the countryside for patriot men to retaliate against. The South was really notorious for this. The Carolinas were split between Loyalist and Patriot followers with neighbors and even families going against each other.
There were loyalist divisions, although I believe they were more like militias than members of the British army proper.
Jasanoff's book Libertys Exiles is an excellent read on the experiences of the loyalists in America pre and post Revolution. She does characterize the Revolutionary War as a civil war, although her book only devotes a small part to the actual war itself. She does tackle all your subsidiary questions however.
Additionally, her definition of "loyalist" is more broad, and includes slaves and Native Americans, complicating the idea of a unified "loyalist" experience. Its a good read for what you're after here.
The American Revolutionary War was in fact the first civil war in this country. The British military comprised of many American Militia units called at that time as the Tories. Most historians estimate that 20% of the 2.5 million white Americans were in this group at the outbrake of the war. Its said that this figure may have grown to 35% at different times during the war depending on how the war was going for both sides. Keep in mind that for the most part half of the 2.5 million Americans avoided involvemnt in the war. As for military service in the British Armies records indicate that about 19,000 Americans were enrolled in the regular army in 50 units with 312 companies. An additial 50,000 served in Loyalist militia throughout the war. Black American records are harder to get a fixed number. Even Lord Dunmore's Ethiopian Regiment enrollment is difficult to number but it is said that about 12,000 Black Americans fought for the british from 1775 to 1783. After the war most of these Americans fled to Canada with the rest fleeing to other British held territories. As for the way these loyalist saw the revolution well to be honest they saw those Americans as rebels. People who threaten their way of life which was very connected to the home country of Britian. Most had something to lose if the rebellion won and some were alienated when these Rebels resorted to violence, such as burning houses and tarring and feathering of outspoken Loyalist. Loyalist feared the chaos and mob rule that they beliefed would be the result of ending British rule.