>>11617223The movies haven't gone super deep, but it has shown a lot of other things.
Predators and AvP have shown that they can be logical, fair, and reasonable, and can communicate through gesture with humans. When Adrian Brody's character saves the Pred that is strung up in the Super Predator camp, the Predator shows him that it knows he is from Earth and is willing to take him back there for saving him. Scar in AvP gestures to Lex that he is going to use the wrist gauntlet as a bomb to destroy the aliens. It even helps her out and fashion's weapons and equipment out of the xeno parts, and even marks her as a warrior for killing the xeno.
Several of the comics are worth reading. I'd suggest looking up the old early 90s' AvP and AvP:War series. Those are the ones about Broken Tusk and Machiko Noguchi. The latter, IIRC shows a lot about how the Preds spar, and shows some other facets of their culture, like how the dishonored preds fare.
Bad Blood is good, because it shows what a, well, Bad Blood is. They're basically the Predator equivalent of a merciless serial killer. It even shows that Predators have something akin to a police force.
The "Fire and Stone" and "Life and Death" series are also great, but they're very long, both spanning four issues each across an Alien, Predator, AvP, and Prometheus series (so 16 issues total, with a 17th issue epilogue, for Fire and Stone, and the same for Life and Death.) those series have the Ahab Predator, who has spent his life trying to hunt down and fight an Engineer. Ahab is kind of hilarious because he ends up getting stuck with a bunch of other misfit humans and spends most of his time cracking--and laughing at--his own jokes in the Predator language.