Without a coat is preposition in " Don't go (without a coat)".
I think the casket is a symbol of death and it is also a symbol of cruelty of the narrator that he took Doodle to see it and touch it to emphasize that they thought he was going to die so needed to be brought face to face with it.
1. C because of the sensory details, Plunging and gloom.
2. A the calmness of the sea...
I don't see the passage, but an antagonist is a villain, or in other words a negative role.