I have in front of me the Shorter Oxford English Dictionary from 1973.
Airplane is shown as an alternative to aeroplane that has been in use since 1907. It is a more recent term for a flying machine than aeroplane (1884), but OED don't regard it as a particularly American spelling.
Regular has a number of meanings, one of which is normal. That meaning is dated to 1638.
Cotton candy is not listed and is definitely North American in origin.
Program was spelt this way when the word was first seen in 1633. The programme spelling appeared when the word was reintroduced from French and is noted as the more usual spelling. They hadn't picked up the use of "program" to mean computer software at this stage.
Often, things people think are Americanisms are not. Years ago, on another thread (which seems to have been deleted), someone asked if using "gift" as a verb and the word "gifted" meaning to give someone something were Americanisms and got very upset when I pointed out that they weren't, both having been in use since the early 1600s.
As others have pointed out, English is a living language. It evolves. New words appear and existing words change meaning, pronunciation and/or spelling. For example, when I was young, "literally" was only used to refer to something that was actually happening. That is the only meaning recognised in my 1973 dictionary. However, the latest OED recognises it as a word used for emphasis - "that was so tasty it literally blew my head off".