Why does this translate to "Nothing happens" instead of something like "It doesn't happen"? Why is the "Es" in there?
"It doesn't happen" would be "Es passiert nicht". If you don't like the 'es' (which is often used in German to express that something happens without an actor) you could also say "Nichts passiert".
So this could never mean "it never happens"?
No, that doesn't seem right. Never = nie. So your sentence would be: Es passiert nie.
Would "Nichts passiert." not work?
What is the subject of this sentence?
And nichts is an object?