There is enough evidence to suggest that Montresor is certainly an unreliable narrator in Poe's classic short story "The Cask of Amontillado." In the opening paragraph of the short story, Montresor states that Fortunato had caused him a "thousand injuries" and "ventured upon insult," which apparently justify his motivation for seeking revenge. Montresor's reason for committing a horrific murder is vague, obscure, and ambiguous. He provides no solid evidence to support his decision, which is unsettling and problematic. If one were to even contemplate burying another person alive, there should certainly be legitimate evidence to even justify the thought of taking that person's life. However, Montresor simply glosses over Fortunato's "injuries" and assumes that his actions are warranted.
In addition to Montresor's vague reasoning for seeking revenge on Fortunato, the fact that Montresor commits murder is further evidence of his unreliability. One could argue that a sane, rational person would never bury another individual alive. Plotting and executing such a horrific crime suggests a degree of mental illness and instability. Another example of Montresor's unreliability takes place at the end of the story. Montresor thrusts his torch in the remaining aperture in the wall and lets it fall in hopes of getting a rise out of his enemy. However, Fortunato does not reply and all Montresor can hear is the jingling of bells. Montresor then mentions,
"My heart grew sick—on account of the dampness of the catacombs" (Poe, 10).
This statement is further evidence to suggest that Montresor is an unreliable narrator. The audience recognizes that his heart "grew sick" as a result of his guilty conscience and tortured soul. Somewhere in Montresor's heart, he regrets his actions and pities his enemy. However, Montresor would have the reader believe that the dampness of the catacombs was the reason his heart grew sick, which is an obvious lie. Overall, one could argue that Montresor is an unreliable narrator because he refuses to give specific reasons to justify his actions, commits a horrific crime, and attempts to conceal his true feelings regarding Fortunato's murder.
While there is certainly evidence to suggest that Montresor is an unreliable narrator—he strongly dislikes Fortunato, he offers no evidence of the wrongs supposedly done him by Fortunato, and so on—I'm going to suggest that he is relatively reliable because of when he is telling the story and the possible circumstances under which he tells it. When he begins to narrate the events, he addresses his audience as one who "well know[s] the nature of [his] soul." It is reasonable to suggest that one who has intimate knowledge of another person's soul must be privy to the most personal kinds of knowledge; a priest who has heard someone's honest confessions would have just such a knowledge. At the very end of the story, Montresor says that it has been "half a century" since he killed Fortunato. He must be an old man by now, and he's kept the secret of this murder to himself for a very long time. What circumstances would compel him to confess it now? Why tell the story fifty years later? Because of his advanced age and the comment he made about his auditor's familiarity with his soul, I offer the idea that Montresor is confessing his sins to a priest while on his deathbed. It would make sense that he is seeking absolution for his sins before he dies, and if this is so then he would be telling the truth (at least, the truth from his perspective and memory). One does not lie in confession, as this defeats the purpose of confession! Thus, it is certainly possible to argue that he has reason to be reliable in his narration.
Montresor is an unreliable narrator. We can't trust what he tells us for several reasons.
To be persuasive, a writer or storyteller (this is apparently a deathbed confession) must meet two criteria. First, his reasons for what he is doing (or has done) must be sufficient. As mentioned in the answer above, Montresor doesn't give us any real reason for why he killed Fortunato. The few reasons he offers—that Fortunato has injured and insulted him—are not concrete or specific. They are not sufficient—not enough—to justify murder, to make us feel that, yes, Fortunato deserved this fate.
Second, to be persuasive, the storyteller must offer evidence that is relevant or relatable. Again, Montresor gives us no evidence that the punishment fits or is relevant to the crime, since we don't truly know what the crime is. Walling him up bears no relationship, as far as we can understand, to what Fortunato has done.
Because Montresor leaves out so much information that we need to evaluate his actions, we can't rely on him. We strongly suspect that were Fortunato or an omniscient narrator to tell the story, or were a reporter to investigate the events for an objective news report, a very different version of the story would emerge.
The narrator in this story is a bit of a crazed, jealous, spiteful man who ends up bricking his friend behind a wall in order to ensure his death, and, he does it all with panache and enjoyment. So, I wouldn't rely too heavily on him-he's not necessarily trustworthy. The story is told from his point of view, so it is first-person, and, because of the things I listed above, he isn't a reliable narrator. He might be relied on to have told the events of the actual story accurately as he can, but before the story occurs, we don't really get an objective picture. For example, why is he so angry with Fortunado, and did poor Fortunado really deserve such cruelty? The only clues that we get to these questions are Montresor's words himself. He states,
"THE THOUSAND INJURIES of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge."
So, we can't say with any certainty that the narrator's reasons for revenge are justified. We don't know the details, and can't make a judgment call for ourselves. Hence, the narrator is a bit unreliable, since his entire mission is based around something that he deems worthy of revenge, without telling us what it is. I hope that those thoughts help; for your other questions, I suggest submitting them separately, since the format of the website allows one question a day. Good luck!