I can't recollect ever seeing "Thank you" hyphenated.
It's very common in BE when speaking of "a thank-you" as a noun or
"a thank-you note" as an adjective, and in this case it is perfectly
correct and grammatical (BE tends to avoid unconnected compounds). I
suspect it would be wrong in AE, where you would prefer "a thank you"
or "a thank you note".
As noted "Thankyou" is occasionally seen in UK writing. I was taught/brought
up to consider it a solecism.
Classically, yes. But some 20th century writers (such as Shaw and
Joyce) avoided both hyphens and apostrophes as a matter of principle,
so in those circumstances, writing it as a single word can also be