"Love the questions themselves."
-Rainer Maria Rilke
If it doesn't, it should. Finding out "why" is a big reason people read on. Your characters don't have to know all of the answers, and neither do you. But you should know many of them. Not while you are writing the first draft, perhaps, or even the second or the third. But when your story is done, your readers should feel as if most of the big plot questions have been answered, otherwise they feel cheated.
That said, it's good to leave a little mystery. And some ambiguity at the end can allow for multiple interpretations that enrich the story. But that is a tricky thing to do--to allow for an open ending that remains satisfying. So think carefully about what you must reveal, and what you must not.
Now let's talk about bigger questions. Philosophical ones.
Does the author need to know all of them?
Many of us write because we, too, just like our readers and characters, have questions. Writing helps us make sense of our world, even when it is at its craziest. It allows us to help others figure things out. It isn't our duty to come up with all of life's answers. After all, as Voltaire said: "Judge a man by his questions rather than his answers."
But if we ask the right questions, with our stories, perhaps we help our readers find their own answers. And maybe, if we are lucky, we find them, too.
"I don't write books because I have answers. I write books because I have questions. What we are is the questions that we ask, not the answers that we provide. It's all about the process of self-examination. I think that's what the best writing always contains."
-John Edgar Wideman