Large numbers of Ulster Scots (commonly called “Scots-Irish” or “Scotch-Irish” in the US) migrated to America during the colonial period: at least 250,000 came between 1717-1775, which according to David Hackett Fisher, was the largest wave of colonial immigration to America prior to independence.

Scots-Irish culture is commonly associated with the South, but they also moved into northern states as well. Delaware & Pennsylvania were their first ports of entry, and there’s a wide range of place names throughout Pennsylvania and New York (Scotland, Carlilse, Donegal, Derry, Ulster County NY, Orange Country NY) which indicate traces of Scots-Irish settlers. By the time of independence, they could be found throughout the American colonies and were often among the first white settlers in frontier regions.

Someone else could speak more to the construction of American national identity in the colonial period and early republic, but in general, distinct ethnic identities that we'd think of today (German-American, Irish-American) did not last very long in the early United States: people most often identified as American or White, and by the time of the Civil War many of the Scots-Irish families had been in the US more than 100 years. I am not aware of any Scots-Irish writers at the time of the Civil War specifically decrying the bloodshed between Scots-Irish people, rather than the nation as a whole.

In answer to your part B, not sure if your timeline or terminology is confused: the Confederacy was formed in 1861, and the American War of Independence was fought 1775-1783 so the Confederacy was not around during the time of independence. Regarding opposition to independence among Scots-Irish people, during the fight for American Independence, there were people called “tories” or “loyalists” who opposed independence, but the Scots-Irish were not overrepresented in their ranks. Leyburn’s history of the Scots-Irish reports that support for Independence among the Scots-Irish was "practically unanimous". The one exception to this was the South Carolina backcountry, which was settled in the 1730s-1760s predominantly by Scots-Irish people, and saw violent conflict between loyalists and patriots. About 1/3rd of South Carolina’s population stayed loyal to the crown (the 2nd highest among the 13 colonies, after New York), with the backcountry region about evenly split. However, historical research on this subject has not found an ethnic explanation for why a person supported one side or the other (see references Klein & Moore below), there were Scots-Irish people on both sides.

References: General discussion of Scots-Irish Americans: Fisher, David Hackett (1989). Albion’s Seed: Four British Folkways in America. Oxford University Press

Leyburn, James (1962). The Scotch-Irish: A Social History. University of North Carolina Press.

Scots-Irish loyalties in South Carolina during the American Revolution:

Klein, Rachel N. (1990) Unification of a Slave State: The Rise of the Planter Class in the South Carolina Backcountry, 1760-1808. University of North Carolina Press

Moore, Peter (2006). The Local Origins of Allegiance in Revolutionary South Carolina: The Waxhaws as a Case Study. The South Carolina Historical Magazine. 107