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.