Are there any writings about the people who live in the southern Dark Lands of the LOTR universe?

The “Darklands” of Tolkien are in the east, not the south.

BTW- I'm writing all this from memory and I can't be bothered to google so OP will have to do that himself.

So when Melkor fled to Middle Earth, he took over Eurasia and Ungoliant the Spider took over Africa. The Darklands were the areas in the East which remained in the darkness for some reason. Possibly he was inspired from Australia- but the imagery is pretty explicitly kitsch White Man's Burden Africa.

There's nothing really specific and cleaned up so OP will have to wait till Christopher Tolkien releases a proper text but in general, the tale of Earendel is what you want.

After enjoying the descriptions of “evil men” (cough - Indians- cough) from the “South” who worship snakes (like yours truly) and ride elephants (like the ancestors of yours truly) and their “evil men” brethren (cough- Chinese- cough) who went on horses Mongol-style, you can read scattered references to all the vivid daydreams of the do-gooding British explorers who civilized Africa with the word of Eru in one hand and the Gatling gun in the other- volcanoes, tree men, pgymies, cannibals, the works.

So were they Sauron-worshipping “evil men” as well?

Considering we are having a full-on renactment of the British Raj and the Boxer Rebellion, to go alongside Fantasy WW1/ Ottoman Wars, I see no reason why there can't be a fantasy Scramble for Africa in the Legendarium.

Yeah, I'd rather stick to Warhammer Fantasy, even with the Sigmarines…