I can speak to the question about the economic impact. Simply put, the "loss" of the American colonies was probably an economic benefit. The Brits saved themselves the expenses of maintaining and militarily protecting their colonies across the Atlantic, and the Americans kept exporting to them anyway.

There's a long line of argument in economic thought that colonialism, at least as practiced by Europeans over the 16th-20th centuries, was harmful both to the subject people and also to the home economies of the colonisers. The basic insight is that it is better to have a more productive trading partner than a poorer one and that colonialism was destructive by its nature, both through direct violence and destruction of physical and social capital and human lives, and indirectly as colonial officers typically were looking to line their own pockets, make a fortune and head home, not a good attitude for a government. This insight was famously stated by Adam Smith in his 1776 work The Wealth of Nations, and more recently is championed by the economic historian Deirdre McCloskey. 

British rule of its North American colonies in the 18th century was, as European colonies went, on the less destructive end. Britain did however ban Americans from manufacturing certain goods including iron, and hats, and Britian required certain colonial exports to only go to itself, these exports included valuable goods like tobacco. Any overall benefit to the British economy would have come from the lower prices in Britain caused by the export restriction (the ban on manufacturing to the extent that it was binding would have made Brits worse off: the higher prices obtained by British manufacturers being offset by higher prices paid by British buyers plus less iron available in total. R. P. Thomas and D. N. McCloskey have a useful summary of the research about the impact of North American (and other) colonies on Britain in their chapter Overseas Trade and Empire. They estimate that the benefit at most from the American empire was about £75,000 annually, out of about total British income of around £140million in 1770, while the costs to British taxpayers were about £400,000 annually. (Page 97). So from this point of view, American Independence was a net benefit to the British public.

This is because the American Revolution did not stop British trade with North America, exports to North America rose from a 6% share of total British exports in 1700-1701 to a 32% share of British exports in 1797-98 (note: these numbers are not comparable with the figures above as the foreign trade figures at the time were reported in fixed prices set in 1700 and thus are best interpreted as changes in volumes). While there wasn't a comparable rise in British imports from North America as a proportion, North American imports did keep their share of total British imports during that time.

Also at this time,  the UK was undergoing the Industrial Revolution. While many writers attribute the Industrial Revolution to the British empire, amongst specialists it is different. The role of trade, all trade, so including with non-colonised countries like France and the Netherlands, in the Industrial Revolution is highly debated, and the consensus is tending towards that it wasn't that important compared to domestic drivers and technological improvements.

In 2008, Daudin, O'Rourke, and de la Escosura summarised research into estimating the impacts of foreign trade on British GDP as "both approaches tend to produce small numbers, with the estimated contribution of empire or trade to growth remaining modest compared with the expansion of the domestic market (page 8). 

In 2014, Clark, O'Rourke and Taylor published a paper estimating that the impact of trade was significantly larger, in the 19th century than earlier estimated, estimating the impact in 1850s of 25%-30% - but even they estimate that in the 1760s, as the Industrial Revolution was still in its early stages, the welfare impact of cutting off all trade would be only 3-4% of national income. And while 25-30% sounds large, British GDP per capita had about doubled between the 1760s and the 1850s.

(Note that these estimates of the impact of trade are of the actual goods and services, many of the new technologies often built on or straightforwardly used ideas developed in other countries, e.g. the British Agricultural Revolution from the 17th to 19th centuries drew on a pool of improved agricultural techniques developed across England, the Netherlands and northern France [including modern Belgium], the French physicist Denis Papin played a role in the development of the steam engine, and of course there were New World crops like the potato, a remarkably nutritious staple, a fact which played a role in the tragedy of the 1840s.)

So to summarise, American Independence in and of itself was probably a mild benefit to the British economy. The American colonies weren't lost, they kept on exporting to Britain. What's more, the British Industrial Revolution was more down to domestic drivers and new technologies than to trade, even accounting for all trade, not just North American trade. 

Sources

Clark, O'Rourke and Taylor, 2014, The growing dependence of Britain on trade during the industrial revolution, Scandinavian Economic History Review (working paper publicly accessible at https://www.economics.ox.ac.uk/materials/papers/13258/clark-et-al-new-world.pdf)

Chapter 4 in Floud and McCloskey, The Economic History of Britain, 1700-Present (1981), Vol. 1, pp. 87-102. http://www.deirdremccloskey.com/docs/graham/britain.pdf

Daudin, O'Rourke, and de la Escosura, Trade and Empire, 1700-1870, July 2008, https://www.ofce.sciences-po.fr/pdf/dtravail/WP2008-24.pdf

Note: the Floud and McCloskey reference is fairly old but I'm not aware of any new research that overturns their results. If anyone is aware I'd be interested.