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Another 2 explanations needed for Bonxie's solutions (I don't have access to today's paper,but presume my suggestions are OK):
18a Philosopher giving an American guitar to the 'appy couple? ANAXIMANDER
21a Christopher Lee finally developing into a high flier KITE Why Christopher=kit?

Kit is frequently used as a diminutive for Christopher - or Christine, come to that.

Many thanks,AJT1:I wasn't sure!

an axe(a guitar)
cockney him and her

Thanks,Trevor:I'm obviously not up-to-date with slang,and the Cockney eluded me in my frenzy!

i don't think Axe, for guitar, is particularly American.
it's more of a heavy metal, rock thing.

Do Americans spell axe as ax?

Perhaps because ax is more frequently used here? (I always spell it axe, however!)

http://www.grammarist.com/spelling/ax-axe/

that would explain the use of 'American ' in the clue, thanks 'risty :)