How was the Red Death able to enter Prince Prospero's castle even though it was sealed in "deep seclusion" from the rest of the world?
Unfortunately, the answer to this question is not in Poe's narrative, which is actually not that surprising. The stories that Poe writes often have mysteries within them, or at least some mysterious aspect involved; in the case of The Masque of the Red Death, this mystery is the presence of the Red Death. Of course, that allows the readers to try to come up with their own answers. For instance, Poe originally describes the Red Death like it is a person, potentially even a guest of Prince Prospero's, and it is not until the character kills the prince and the remaining crowd fall upon him that we learn that the killer is not a person at all, but an intangible figure somehow holding up the clothes and mask. So he could have potentially inhabited other clothes from the very beginning, making people think that he was just another guest; he could also have shown up and slipped through a crack or some other structural weakness of the abbey because he has no tangible form, he is just a disease. Of course, it was very naive of the prince to believe that he could lock himself in an abbey to keep himself safe from a disease, which could very well have been airborne, or transferred by animals. There are countless ways that the intangible disease could have made its way into the abbey and the masquerade, and Poe leaves it to your imagination to decide.