What if the mall owner or manager felt he knew the official well and assumed that he would prefer the protesters be removed? If he had them removed without any communication with the official would that be a violation?

It primarily depends on who is funding the politician's venture within the mall. If it's the taxpayers then that removal would constitute a First Amendment violation even without direction of the government itself.

Which is why your local reps office isn't inside a mall, because the mall wouldn't want the unblockable distraction of protesters or public events.