When you run trails, there’s a balance to strike between gawking at your beautiful surroundings and staring at the ground to avoid tripping. Regular trail running improves your proprioception, or your sense of your body’s placement in space. With more trail running, you get a better instinctual feel for obstacles on the ground and how to run on, over, or around them. Improved proprioception, like improved balance, should help all of your running, especially when you’re running in the dark and lack as many visual cues about your surroundings.
On trails, run with a light, quick stride that’s a bit shorter than you would use on flat, unencumbered terrain.
A good running shoe is a good running shoe, period, and should work fine on most trails. Some people like to wear sturdier shoes on trails, but I think the opposite approach makes more sense—you want a light, low-to-the-ground shoe that will increase your agility. It’s the same rationale as choosing minimalist orienteering shoes over high, heavy hiking boots for walks in the woods.