why the machine's stopped
Neo is developing psychic abilities that are connected to his control over the matrix. His mind can reach out to the machine world even without the help of the electronics on the ship. He doesn't have a lot of control in this regard, which is why his mind gets stuck in the machine-world loading program (the subway).

what Zion actually is
It's the last city on Earth where humans live free. But it's also some sort of mystical breeding ground that the machines leave in place long enough to breed a new "One." Then they kill all but a few of them and repeat the cycle. Neo breaks the cycle by being more powerful than they expected.

I'm not really clear on why the cycle is supposed to be important to the machines. It has something to do with them using the free will of the One to help reprogram the matrix, by forcing him to make a choice (save Zion or save Trinity). The machines apparently have no free will of their own, so they must use a human for this ingredient.

who the oracle is and how she knows what she does
She is simply a program that runs inside the matrix. One assumes she knows a lot because the program has access to all of the data inside the matrix.

and why the hell is Trinity so ugly and why didn't Neo dump her for the Vampire Persephone chick?
Trinity is not ugly... she is ugly-sexy, and there is a huge difference! Sure, she's a little too goth, but who isn't in the world of the matrix? Persephone is of course only a program, so Neo couldn't have much fun with her in the real world. ... besides, it's twue wuv!