The word used in the situations you described is (transliterated) yada, which simply means "to know" and is often translated (in different circumstances) find, understand, comprehend and acknowledge.
Considering some of the situations presented in the Old Testament (drunken incest of Lot and his daughters, rape of Dinah, rather suggestive imagery in Song of Solomon, etc), I doubt euphemisms would even be considered necessary; however, Strong's concordance suggests it is used euphemistically (in addition to other senses) in the Hebrew.
I imagine those who translated earlier (KJV) would not have seen reason to translate yada any differently when it referred to sex (they rarely translated words differently solely for the sake of clarity), whereas newer translations (NASB), more for the sake of clarity than anything, use another euphemism (ie. had relations with). I doubt any translators would find a reason to change a euphemism in the original language into something more graphic.
1. Did "long time no see"
arrive in U.S. English from forms of pidgin English
spoken separately by both some Native Americans
and some Chinese immigrants?
The earliest recorded examples are from native Americans, but it's plausible it was used in other types of pidgin English at the same time.
2. When did this
turn of phrase first gain the recorded notice of an
American English-speaking author?
It has been recorded by American English-speaking writers in 1900. The author Raymond Chandler used it in a 1939 newspaper and 1940 book.
3. When did the phrase cross over into use by native U.S.
English speakers among themselves?
Chandler presumably helped popularise it with detective stories and film noir of the early forties.
The OED says it's a "Colloq. phr. (orig. U.S.) long time no see, a joc. imitation of broken English, used as a greeting
after prolonged separation."
Their earliest quotation is 1900 from a native American:
1900 W. F. Drannan Thirty-one Years on Plains
(1901) xxxvii. 515 When we rode up to him [sc.
an American Indian] he said: ‘Good mornin. Long
time no see you.’
Their next quotation of 1939 shows it was fully naturalised:
1939 R. Chandler in Sat. Evening Post 14 Oct. 72/4
Hi, Tony. Long time no see.
Their next is also from Chandler, in 1940's Farewell, my Lovely.
Best Answer
The concept of "husband's tea" may have originated as a description of tea that is not good enough "for company" (or for oneself) but adequate for the needs and indiscriminate tastes of one's spouse. An early instance appears in Lady Rosina Lytton Bulwer, The Budget of the Bubble Family (1840). The summary description of chapter 6 contains the following fragments:
The portion of the chapter to which the "Husband's Tea" snippet refers is this exchange in a confectioner's shop:
Most other early instances emphasize not the inferior quality of "husband's tea" but its weakness, as if the term referred to a second pot of tea made with leaves already used once. This usage occurs twice in The Earthen Vessel: And Christian Record and Review (1850), cited in user240918's answer—first in "Snows' Fields Meeting on Behalf of the Christian Poor Society" (page 49):
—and second (in what might be read as a response to the first instance) from "The Saviour's Solemn Caution Against the Sin of Covetousness Now So Prevalent in Our Professing Churches" (page 167):
Likewise, "The Gambler," by M.A.B. in The Family Herald: A Domestic Magazine of Useful Information and Amusement, volume 10 (December 3, 1853) has this reference to "husband's tea" in the context of a visit by Mr. Warrener to the home of Charles and Agnes Morton:
And from a brief item originally printed in Mother's Friend, reprinted in The Christian Miscellany, and Family Visitor (November 1854):
In a similar vein—but somewhat later—from Thomas Plowman, Acis & Galatea, or The Beau! the Belle!! and the Blacksmith!!! (1869):
John Hotten, The Slang Dictionary: Etymological, Historical, and Anecdotal (1874), which both WS2 and user240918 allude to in their answers, includes this entry for "water-bewitched"
The entry for "husband's tea" in Report and Transactions of the Devonshire Association for the Advancement of Science, Literature and Art, volume 9 (July 1877)—cited by the OED in the excerpt that WS2 includes in his answer—is included in "First Report of the Committee on Devonshire Verbalk Provincialisms" and reads as follows:
As Hotten's definition indicates, there is some inherent ambiguity regarding whether the weakness of "husband's tea" is owing to a lack of virtue in the leaves themselves, severe parsimoniousness in the doling out of fresh leaves for a potful, or a requirement that the leaves do double duty on a second ("husband's") pot. According to "The Word on the Waters," in The Quiver (1887), reuse is commonly the culprit:
But I suspect that different speakers may have had different causes in mind. And although Lady Lytton Bulwer's suggestion that "husband's tea" is simply tea of too low a grade to be served to important people may be the earliest recorded instance of the term, it may be that she misunderstood the sense of the term as used in common parlance because she couldn't imagine someone skimping on—or reusing—the essential ingredient.