I don't understand 「僕は誰より彼女が好きなんだ。」. I guess 好きなんだ means love, but なん means not. Can anyone help me?
なん does not mean "not". This (な)ん is something called "explanatory-の". You can learn about it in the following articles.
より is a particle to mark a comparison target. So the sentence is the same as 僕は誰より彼女が好きだ but with an added nuance. Perhaps the person is trying to convince someone. The translation would be "I love her more than anybody (else)."