What is the nature of intelligence?

My whole life I have always thought of myself as intelligent; indeed as a genius. I have done pretty much nothing with my life so far aside from learn, but I am still young.

What is intelligence? Is it innate, learned, or both?

Am I more intelligent than you, and if so, how can we prove or disprove that?

Are there really several types of intelligence, as wishy washy psychoanalysts claim?

Would the ultimate test of intelligence being two players playing a game they have never played before (involving principles they have never encountered before?)