"Anymore" as a single word definitely exists. It's used by native speakers in negative sentences: "I won't talk to him anymore." "Any more" is used in questions or investigations: "Would you like any more tea?" or "We'll see if there are any more potatoes."

"Anymore" certainly is a correct word--it has been a very long time since using one word was "wrong" and using two words was "correct" (there are over 300 million examples of "anymore" on the web, according to Google, and every dictionary recognizes it as a correct spelling). As for the usage, "anymore" means "any longer" (example: "India is not a colony of Great Britain anymore"). "Any more" means "additional" or "extra" (example: "I don't have any more candy, my brother ate it all").

There is no such word as "anymore". It is simply a misspelling. "Anymore" and "any more" are two ways of spelling the same thing, and the two have the same meaning.

Typically in the USA "anymore" is used to mean "nowdays". However I believe British English classifies them as either having the same meaning, or simply does not recognise "anymore" as valid spelling. To be safe I would just use "any more".