You are right. In the dark forest, the predators must eventually die out, because they can't find prey.
No. It's not really a predator-prey relationship, because the predators aren't consuming the prey for sustenance. They are killing out of self-defence only.
Some predators can go weeks to months between feeding. Some snakes, some spiders. Now consider some lovecraftian horror.
No. It's not really a predator-prey relationship, because the predators aren't consuming the prey for sustenance. They are killing out of self-defence only.