Colonel Creighton is evidently high up in the British Secret Service, but Kipling is deliberately vague as to his role and position. Although Mahbub Ali addresses him as 'the head of the Ethnological Survey', there is no such department in recorded existence.
In this passage, Creighton bids Kim learn the art of cartography at St Xavier's. Map-making skills would have been crucial for British agents gathering intelligence for use against the Russians. By 1865 the British had secretly begun mapping Tibet, which had become a major focus of the Great Game, and had banned all foreigners from entering. Trained Indian surveyor-spies disguised as pilgrims or traders mapped their travels across the Himalayas to Tibet, where they took readings at night.
The professional dancing-girl that aids Kim with his beggar-boy disguise is a Nautch girl. Nautch girls traditionally perform secular dances for the pleasure of their audiences, rather than in holy places.
During the nineteenth century, Nautch girls often doubled as prostitutes. That Kim has escaped to a brothel is implied by Kipling's allusive reference to the abode as a 'certain house' and through a woman's exclamation: 'Doest thou know what kind of woman we be in this quarter?'