I completely agree with leaving Shivans an enigma, after all, it is not death we fear, but the unknown.
Predators' (or, as the call themselves, Yautja) homeworld is a cold, hard planet where living is very difficult.
Predators often fight creatures far stronger than they are (they developed advanced technology to counter that) and they live on top of vertical structures like trees (see how good climbers the are, and how they prefer tall buildings).
The world itself is far from their home star (Predators can see almost nothing but a red screen, because almost no light enters tha atmosphere) , but somehow it is a hot planet (Predators prefer hunting when the heat is turned on)
Alien planet is esencially water, since Aliens (Xenomorphs) are very good swimmers, and the landmass is filled with mountains, since they are very good climbers. Aliens may not be the main species of their world, since they are parasites, this means they coexist with more dangerous, smarter or bigger animals.
Aliens' world is prone to intense climatical variations, since Aliens adapt to the weather they are very quickly.
Also, Aliens have an ability called "assimilation", and allows Aliens to combine their DNA with other species by Facehugging a specimen (this explains the PredAliens)
Aliens may coexist with Predators