Epistemology is the study of Knowledge. What we know, and what we don't, and the definition of Knowledge. It's very interesting.
Nihilism is the belief that nothing exists, and can be viewed in the ontological/metaphysical/ethical sense.
When it comes to ethics and morality, Nihilism assumes that if God doesn't exist, there is no such thing as an objective morality. (Nietzsche had a pseudo-nihilistic philosophy, which was that if God doesn't exist, then there cannot be a rational basis of morality. And even if there was, it would be an unintelligible concept to us).
In every other sense, Nihilism is the belief that nothing exists in general. It's a bit wonky.
Solipsism however isn't a study of ethics. It's the metaphysical belief that nothing other than your mind exists. And that you can't trust your senses. It's got a bit better logic than Nihilism does, but it's pretty useless. It does have some consequences ethically however.
And finally existentialism, is the philosophical stand point, that all life is meaningless, until you, your self give it meaning. And no one else can give your life a purpose, or meaning.
Yeah, I love this stuff
