Before leaving for England, Tissot was a painter of Paris society, a practice he continued with English society until the death of his beloved Irish mistress who was the mother of his son. During the 1870-71 Franco-Prussian War and its Paris Commune aftermath, he was in Paris and helped fight in its defense. The Wikipedia biography linked above is unclear as to why he left France. One explanation is that it was because he fought on the Communard side, and the Commune was, of course, violently crushed by French forces. The entry offers the suggestion that Tissot joined the Commune side as a means of protecting his assets. This makes some sense because he almost universally featured well-to-do people and their haunts in his paintings, something unlikely for a committed revolutionary. Plus, towards the end of his career, he switched to making watercolors of religious subjects, something favored by conservative and Royalist groups in late 19th century France.
Tissot's mature oil painting style can be described as generally hard-edged so far as his subjects are concerned; background objects were often treated less distinctly. Perhaps because of his sharp rendering, his London-era paintings are a useful resource regarding aspects of England in the 1870s and early 80s.
Tissot visited London years before he moved there.
According to its Wikipedia entry, the Calcutta was an 84-gun second rate (in terms of broadside) Royal Navy vessel. Being thoroughly obsolete years earlier, it became a gunnery training ship at Devonport in 1865. Devonport is a ways west of Portsmouth, so either the painting's caption is wrong or it's Wikipedia at fault. Regardless, it seems that the stern of the ship was still serving as a site for social functions when Tissot depicted it.
The word is from the Irish, and means "my darling." The women pictured is Kathleen Newton, Tissot's mistress.
Note the similarity of the subjects in these two paintings.