What's the difference of...
¿No te gusta el arroz? and ¿No gustas el arroz?
¿Quieres un sombrero? is correct. Can I ask " No quieres un sombrero?" If so, why "¿No gustas el arroz?" is wrong?
And what's the difference of tú and te?
In English we like things. In Spanish they please you. So, when asking "te gusta el arroz?" the rice is the subject of the sentence. You are asking the other person if rice pleases them. Te is used instead of tú because te is an indirect object pronoun... The other person isn't doing anything, the rice is. That said, if you use gustar de it is technically correct but Spanish speakers tell me it isn't common. For example, it could be reworded as "¿No gustas del arroz?", but I wouldn't worry about that while you are a beginner.
The second one is incorrect. It literally means that you don't please the rice. I don't think that I have ever heard it but it may be slang in some areas.
Thanks. I thought they both mean "You don't like rice?". I remember some sentences you can leave out "tú".
That is true. In Spanish the pronoun (tu, el, ella, etc) only needs to be included to clear up ambiguity but this verb is reflexive, so it cannot be stated like the above an make sense. Just remember what ever pleases you, you like. Whatever you please, it likes you.