Learn Dutch: De beroemdheid mag dan wel de roem hebben, maar zij is onzeker. - The celebrity may have the fame, but she is insecure.

In this sentence, mag doesn't mean "is allowed to" (giving permission). Instead, it acts as an epistemic modal, which means it concedes a point or acknowledges a fact. When you combine mag with the particles dan wel (literally "then indeed" or "then well"), it creates a strong, set phrase for concession: "[Subject] may well [verb]". It sets up an expectation that a contrasting point is about to follow.

Could I use kan instead of mag to say "The celebrity might have the fame"?

While kan expresses a general factual possibility ("It is possible she has fame"), using mag specifically sets up a rhetorical concession. You use mag dan wel when you are admitting a fact solely to contrast it with a more important point in the next clause. Kan wouldn't convey this "Yes that is true, but..." attitude.

Why is the word order maar zij is instead of maar is zij? Doesn't the comma usually trigger inversion?

A comma itself doesn't trigger inversion; it's the type of word that follows it. Maar (but) is a coordinating conjunction. Coordinating conjunctions (like en, maar, of, want) occupy "position zero" in the clause. Therefore, the subject zij takes the first position, and the verb is stays in its normal second position.