Richtig ist: You don't love me anymore.

AFAIK, in BE it's any more (two words).
Having said that, I keep seeing anymore written as one word. New fashion? Americanism?

cont.

Dein erster Satz ist nicht richtig: doppelte Verneinung

Und wie kann ich mir dabei sicher sein? Gibt es eine Regel die man hier anwenden kann?

Wenn ich nach den einzelnen Übersetzungen google kriege ich bei allen viele Treffer. Anscheinend werden sämtliche Varianten verwendet.

You don't love me any more => 1.150.000
You don't love me anymore => 471.000
You don't love me no more => 385.000

I just found this on Merriam-Webster:

Anymore:
Although both anymore and any more are found in written use, in the 20th century anymore is the more common styling. Anymore is regularly used in negative , interrogative , and conditional contexts and in certain positive constructions...

@ #5:
Then I'll assume that the BE version (at least in the 20th century, as neither I nor my dictionary are THAT old) is/was any more and that more recently the trend is towards anymore, maybe as an American trend. (MW gives US usage).

@ #4:
The reason you get "hits" with you don't love me no more is probably because English like this (i.e. non-standard) is often used in song texts or by other speakers of English (maybe Caribbean, for instance).

"You don't love me any more" is the correct one.