Fortunato ends up being confined in a remote corner of the catacombs, left to his fate. There's no way out for him, and he's essentially trapped in a hopeless situation.
The name Fortunato is significant as it creates a contrast between what one might expect from the name and the character's fate. It also helps build suspense and mystery throughout the story.
The timing isn't clearly stated. However, one could infer that it's been long enough for Montresor to have composed his thoughts and perhaps feel less immediate guilt or remorse.
Poe's use of scientific concepts in his stories makes him a founder. He introduced ideas like the power of the mind and abnormal psychology in his works which were quite novel then.