Page 7. " the Wonder House, as the natives call the Lahore Museum. "
Lahore Museum
GNU Free Documentation LicenseLahore Museum - Credit: Shazee Master

Lahore Museum in the Punjab, Pakistan, was established in 1894 and is one of the major museums of South Asia.

Colloquially named ‘The Wonder House’, Lahore Museum held special significance for Rudyard Kipling as his father, John Lockwood Kipling, was one of the museum’s most renowned curators. The collection, notable for its Buddhist artefacts, also houses musical instruments, jewellery, textiles, pottery and arms that date back to the Mughal and British eras.

Page 11. " Kim gave him no title – such as Lala or Mian. He could not divine the man’s creed. "

Having never set eyes on a Tibetan before, Kim refrains from using the respectful titles of Lala (for Hindus) or Mian (for Muslims). Kim's failure to determine the Tibetan’s race or caste gives some indication of the separation during Kipling's time between the valley people of South Asia and the Tibetan Pahari (hillmen).

Page 19. " We know the arrow fell! We know the stream gushed! "
Gautama Buddha, statue
Creative Commons Attribution Share AlikeGautama Buddha, statue - Credit: Mistvan, wikicommons

The Lama is searching for the River or Well believed to have been created when Siddhārtha Gautama, the founder of Buddhism, loosed an arrow into the ground during a competition to win a bride. 

From The Life of Buddha by A. Ferdinand Herold, tr. by Paul C Blum [1922]:

Then they brought out the bows, and skillful archers placed their arrows in targets that were barely visible. But when it came the prince's [Siddhārtha Gautama's] turn to shoot, so great was his natural strength that he broke each bow as he drew it. Finally, the king sent guards to fetch a very ancient, very precious bow that was kept in the temple. No one within the memory of man had ever been able to draw or lift it.

Siddhartha took the bow in his left hand, and with one finger of his right hand he drew it to him. Then he took as target a tree so distant that he alone could see it. The arrow pierced the tree, and, burying itself in the ground, disappeared. And there, where the arrow had entered the ground, a well formed, which was called the Well of the Arrow.

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Page 19. " one attains freedom from the Wheel of Things "

The Wheel of Things refers to the Bhavacakra or Wheel of Becoming. The Bhavacakra represents the Buddhist concept of Saṃsāra: the cycle of birth (jāti), followed by decay and death (jarāmaraṇa). Buddhists believe that all beings in the universe are enslaved by the Wheel of Becoming, which can only be escaped through enlightenment.