It is contrary to eNotes policy to answer more than one question per posting. I suggest that you enter each question as a separate one in order to have a better chance of getting them all answered.
I will try to answer #3, since that has not been asked before--or at least has not be asked recently.
The setting of the Carnival identifies the city as Venice, which is famous for its annual carnival, nowadays a huge tourist attraction. It also serves as a contrast to the underground setting where most of the action will take place. The carnival also explains why Fortunato is so drunk--and it is essential for him to be drunk, and to remain drunk, for Montresor to be able to trick him and manipulate him as he does.
Most importantly, a good story has to contain a conflict, a problem that must be solved. The whole problem for the protagonist, Montresor, is to lure Fortunato down into the catacombs and chain him to the rock wall.
I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser.
Montresor has to make up a story about a cask of Amontillado which will get Fortunato to come to his palazzo and down below. The problem is complicated by the fact that the streets are crowded with people and Fortunato is wearing what is perhaps the most conspicuous costume in the entire crowd.
The man wore motley. He had on a tight-fitting parti-striped dress and his head was surmounted by the conical cap and bells.
Even ringing bells! It doesn't matter so much if people recognize Fortunato--as long as they don't recognize Montresor. The fact that Fortunato is so conspicuous actually works to Montresor's advantage, because he is dressed all in black and must seem like a mere shadow. Furthermore, in the third paragraph Montresor, whose name is French, disassociates himself from Italians.
Few Italians have the true virtuoso spirit....Fortunato, like his countrymen, was a quack, but in the matter of old wines he was sincere.
So Montresor is cold sober and not participating in the carnival revels. He is not well known, like his intended victim. He can, and does, manage to steer Fortunato to his palazzo and down into the wine celler leading to the catacombs. There he keeps him drunk by giving him two bottles of French wine. When he finally shuts the padlock on his prisoner he has solved his main problem. But dramatic suspense must be retained until the very end.
Fortunato tries to talk his way out of his trap. He pretends to think it is a practical joke and that he is amused. He sobers up very quickly because of his fear and shock. Finally he says:
"But is it not getting late? Will not they be awaiting us at the palazzo, the Lady Fortunato and the rest? Let us be gone."
He wants Montresor to think that a lot of people are expecting him at his home and that relatives, friends, and servants will be out looking for him if he doesn't show up. But Montresor has already established when he first encounters Fortunato that his victim has no "engagement." Twice Montresor inquires about that possibility:
"As you are engaged, I am on my way to Luchesi."
"I perceive you have an engagement. Luchesi"--
The second gambit elicits the the information Montresor needs in order to be sure his victim will not be missed that night. Fortunato says:
"I have no engagement; come."
And his fate is sealed.