It is related of Thackeray, that he was once asked how it happened that the good people in his novels were always stupid, and the bad people clever. To this the great satirist replied that he had no brains above his eyes. (p. 4)
I can't trace this any further back than Henry A. Beers (From Chaucher to Tennyson, p. 206)
Thackeray is the equal of Swift as a satirist, of Dickens as a humorist, and of Scott as a novelist. The one element lacking in him — and which Scott had in a high degree — is the poetic imagination. "I have no brains above my eyes" he said; "I describe what I see." Hence there is wanting in his creations that final charm which Shakspere's have. For what the eyes see is not all.
Neither this reference nor any other I could find puts the quote in the context given by Smith.
There is a wood-cut depicting an oak tree, in the outlines of which the observer is invited to detect a profile of Napoleon on the island of St. Helena, standing with bowed head and folded arms. (p. 5)
It's not actually an oak tree, but this must be the image Smith has in mind.

Mr. Meadows (p. 5)
Probably James Joseph Meadows (1835-1914), an English missionary to China.
Lord Elgin's reply to an address from the merchants of Shanghai (p. 7)
James Bruce, 8th Earl of Elgin (1811-1863), High Commissioner to China from 1857 to 1861, received a welcoming letter from the British merchants resident in Shanghai on March 29, 1858, and replied the next day. The original address and his reply can be read here.
a whole parliament of authoresses of "Domestic Economies" (p. 15)
I at first assumed that "Domestic Economies" was the title of a book or periodical to which many women contributed articles, but I can't find any such publication. Perhaps the plural "Domestic Economies" means "works entitled Domestic Economy," of which there were certainly no shortage in the 19th century.
inscriptions written on paper loosely basted upon a silk background (p. 15)
That is, sewn with loose stitches so as to hold the paper and silk together only temporarily.
Dr. B. C. Henry's "The Cross and the Dragon" (p. 16)
Cross and the Dragon or Light in the Broad East, by B. C. Henry and Joseph Cook (1885). A limited preview is available from Google.
This comes up the Peiho from Tientsin, and is discharged at T'ung-chou. (p. 18)
That is, it comes up the Hai River from Tianjin and is discharged at the Tongzhou District of Beijing.

the maxim which John Wesley named as the rule for a successful church — "All at it, and always at it." (p. 20)
Quoted in many places as a favorite motto of Wesley's. I haven't been able to find the original.
the Trimetrical Classic (p. 21)
Foochow … Honan … Anhui (p. 22)
Ningpo (p. 26)
Sir John Davis was quite right in his comments on the cheerful labour of the Chinese (p. 26)
The Anglo-Saxon needs no scriptural hint to enable him to see the importance of doing with his might what his hand finds to do (p. 27)
if Solomon was right in his economic maxim that the hand of the diligent maketh rich (p. 27)
those fundamental qualities … enumerated as "constant virtues" (p. 27)
a very large percentage of fortiter in re, but a very small percentage of suaviter in modo (p. 28)
Suaviter in modo, fortiter in re — Latin for "gently in manner, firmly in action."
the punctilio (p. 28)
The Book of Rites (p. 31)
According to the distinction described by Sydney Smith, the world is divided into two classes of persons, the antediluvians and the post-diluvians. (p. 36)
Tennyson's "Brook" (p. 37)
Non est inventus is the appropriate motto for them all. (p. 39)
the scriptural motto, "The Lord bless thy goings out!" (p. 41)
the late lamented Dr. Mackenzie (p. 41)
Shan-si … Chih-li (p. 44)
Mr. Baber's "Travels in Western China" (p. 46)
Yunnan (p. 46)
Mr. Little's "Through the Yang-tse Gorges" (p. 46)
a compradore (p. 55)