Just giv'er mate! Getting used to nighthiking is something you gotta do with experience. Like how you get used to the noises sleeping at night and learn which is a squirrel, the wind, yourself, etc, Gotta do the same thing for hiking.
You'll see a lot of eye's looking at you, they're only Deer. Deer (in the dark) have clear white eyes, and may move up and down to get a look at you, nothing to worry about. Bears will be moving more, and have brownish eyes, but they have good hearing, so if playing some music or talking with yourself they leave before you can see them. If you see Blue or Green-ish eyes, especially up in trees, it could be a mountain lion and you're in trouble, or like a marmot or something which I've seen around.
Always recommend a really goddamn bright headlamp, or even a good flashlight.
Try to focus on the trail instead of your surroundings. If you notice yourself looking side to side rapidly feeling real spooked, gotta stop walking and get yourself together. 99.9% of the time the creature moving about, or the snapping noise you heard is a squirrel.