This does not fully answer your questions, but is of interest:
https://warfarehistorynetwork.com/20...yal-air-force/
I don't think any of them "temporarily" gave up US citizenship since for the most part they never said they were Americans, rather they "claimed" to be Canadians, etc.
While nothing is said about pay rates, I would be very surprised if they were paid any differently.
By the time the Eagle Squadrons were being formed the U.S. government had decided to "ignore" the citizenship issue.
https://www.historynet.com/a-few-ame...of-britain.htm
"By the fall of 1940, dozens of Americans, inspired by the widely reported exploits of RAF pilots that summer, were defying American neutrality laws and making their way to Britain. (In 1941, as the first Eagle squadron garnered hugely favorable publicity in the United States, the State Department decided not to prosecute any of the American pilots in the RAF, no doubt for fear of a public outcry but also because isolationist sentiment in the United States was waning.)"
This site (while at the moment seems very slow) has several links also:
https://www.rafmuseum.org.uk/researc...air-force.aspx
A review of the book "The Few" by Alex Kershaw:
https://www.denverpost.com/2006/11/2...-save-britain/
He says they were paid $80 a month.