When the Doctor and Bill are both under water, we clearly see the creature's mouth as looking like the one of a whale.
At the end, when they free it, we see it again and it's radically different, looking like a piranha this time.
The diving suits used by The Doctor and Bill were obtained locally (not part of the TARDIS' manifest) and therefore could not have had their own air supply.
The episode is set in 1814 but the Union Flags shown in the background of several shots are the pre-1801 Union Flag, i.e. they do not include the St. Patrick's cross which was used to represent Ireland which entered a full political union with Great Britain in 1801.
Bill says that she has never seen anyone die before, but in The Pilot (2017) she is present at a Dalek battle where people are killed.
Bill worries about being treated as a slave on account of her colour. But the vast majority of the small non-white population in the British Isles at that time were free. The only ambiguity was about people who had been brought to Britain after being slaves in the British West Indies. The courts were inconsistent, sometimes saying they were still slaves and sometimes denying it.
Bill might well not know this, but The Doctor should have reassured her on the point.
Bill might well not know this, but The Doctor should have reassured her on the point.