Learn Dutch: Die acteur mag dan wel privileges hebben, maar hij heeft geen privacy. - That actor may well have privileges, but he has no privacy.

Normally, mogen means to be allowed to. However, here it creates an epistemic modal concession, functioning just like the English 'may'. When paired with dan wel and contrasted with maar, mag simply acknowledges a fact as true before introducing a counterpoint.

What is the exact function of dan wel here? Could I leave it out?

The particles dan wel strongly emphasize the concession, equivalent to the 'well' in 'may well'. While you could technically drop them and just say Die acteur mag privileges hebben, adding dan wel is the standard way to set up the expected contrast with maar.

Why doesn't the word order invert after maar?

The word maar is a coordinating conjunction, meaning it joins two main clauses without altering the word order of the second one. That is why the second clause starts with the normal subject-verb order: hij heeft.

Why do we use geen instead of niet to negate the privacy?