The Tsar knew that the hermit met only common people. So he dressed himself up as a common man by putting on simple clothes and dismounting from his horse he went alone to meet the hermit. It can also be argued that perhaps he knew that concealing his true identity from the hermit was not possible. But he did not want to use his power and position before the wise hermit. He respected the hermit’s ideals.
Yes, I think the hermit knew that it was the Tsar in the disguise of a common man. It would be too naive to believe that someone like the hermit with such profound wisdom could have been deceived by any kind of tricks. For him it did not matter whether it was the Tsar or a common man. All were equal to him.