Answer:
"She found her cabin still dry, but as she rummaged about, she heard a key turn and suddenly realized the steward was locking the stateroom door <u>to prevent looting</u>."
This is the excerpt that best supports the idea that there is a sense of mistrust on the ship because the caption or somebody who is in charge of the ship probably thinks that the passengers will try to escape their own room to go into another person's room and steal one or a few of their possessions from their original owner, so in able to stop that from happening, the person in charge told the stewards to lock their doors.
Explanation:
"When Assistant Second Steward Wheat noticed Chief Steward Latimer wearing his lifebelt over his greatcoat, he urged the Chief to put it under the coat—this made swimming easier."
This one is just talking about the Assistant SSW noticing that CSL was wearing his lifebelt the wrong way and has nothing to do with trust and the ship.
"The water was slowly crawling up the stairs, and from time to time Lightoller walked over to the entrance and checked the number of steps it had climbed."
I think this one is talking about how the flood that was happening begin to make its way up the stairs. This one doesn't have anything to do with mistrust. If it was, I'd think that it would be talking about the people themselves on the ship, not how water is flooding in.
"An old lady made a big fuss at No. 9, finally shook off everybody, and ran away from the boat altogether."
This one is about a lady making a fuss and running away from everyone since maybe she has had a enough and she's probably a bit overwhelmed and such by what is happening. It's not a matter of mistrust, it's just that she felt the need to get away before everything became a bit too much for her even more.
