Learn French: Le goût de ce fruit cru ne me dérange pas. - The taste of this raw fruit does not bother me.

No, they serve different purposes. In ce fruit (this fruit), ce is a demonstrative adjective that points to a specific masculine noun. In the phrases ce qui and ce que (meaning "what" or "that which"), ce acts as an indefinite pronoun meaning "the thing."

Why is the word order "ne me dérange pas" instead of "ne dérange pas me"?

In French, object pronouns like me (me) almost always go immediately before the verb. When you make the sentence negative, the ne and pas go around the whole pronoun-verb group like a sandwich. So, it becomes ne + me dérange + pas.

Why does the adjective "cru" (raw) come after "fruit"?

Most descriptive adjectives in French go after the noun. Only a specific group of common adjectives—usually dealing with Beauty, Age, Goodness, or Size (the "BAGS" rule)—go before the noun. Since cru describes a physical state or category, it follows the normal rule and goes after.

"Dérange" looks a lot like the English word "derange". Is it a false friend?

Yes! While "deranged" in English means insane, the French verb déranger simply means "to bother" or "to disturb." For example, a very common polite phrase is désolé de vous déranger (sorry to bother you).