"anyone" appeared from fusion of "any" and "one"
today "anyone" is an independent word which means "any person or any representative of a group"
The two-word form "any one" is not the same as the one-word form "anyone" and the two forms cannot be used interchangeably.
"Any one" means ‘any single (person or thing)’, as in: not more than twelve new members are admitted in any one year
"anything" refers to a thing, no matter what (except living things)
"any thing" is rarely used and may refer to a particular "thing" E.g. have you seen any of these things? "thing" here may be anything which is allowed by the semantics of the word "thing"