Khan says Paris was subjected to "nightly bombing raids". Paris was not heavily bombed between 1940 and 1944, with limited raids mainly on factories on the outskirts of the city. Paris was declared an open city in 1940 to prevent either side attacking the historic buildings.
There are street lights and many building lights visible in Paris during the bombing raid. Paris had a strict nighttime blackout from 1940 until the end of the war.
When The Doctor meets The Master at the top of the Eiffel Tower in Paris, the light of the lift is seen ascending inside the tower to the level of the top platform. The Doctor is seen exiting the lift and walks round to meet The Master. The lift and power cables in the Eiffel Tower were cut by the French in 1940. The tower was closed to the public during the occupation and the lifts were not repaired until 1946.
Khan asks if the "fascists" win WW2. At the time, the term fascist only referred to the Italian regime. It was not applied more broadly to include the Nazis until after the war.
Ada Lovelace most certainly would know what computers are - people working in teams to perform mathematical calculations by following a fixed set of rules - since this profession (established in the Renaissance) is what Charles Babbage hoped to automate, though success was not achieved until the invention of electrical computers.