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.
I've often heard walk back used idiomatically to mean backpedal from or retract a statement or promise.
A search of the Corpus shows that using walk back in this way is more often spoken rather than written.
Best Answer
Internet searches for "tough titmouse" produce very little of substance aside from discussions of episode 4 of season 2 of The Good Doctor, which is titled "Tough Titmouse" and initially aired on October 15, 2018. A recap of the episode on CelebDirtyLaundry.com indicates that the expression was used in a character's foster family, twice by the foster mother and once by the foster son:
You can view the third instance noted above in a brief Facebook video excerpt, but be prepared for community-theater-level dramatic acting.
In each of these instances, "tough titmouse" doesn't allude to a proverb or other cultural back story involving a tufted (or any other species of) titmouse; it is just a quasi-euphemism for a cruder expression that is itself simply a dismissive expostulation. Presumably, the foster mother in The Good Doctor settled on "tough titmouse" as being more presentable than "tough titties," which, as Jason Bassford points out in a comment above, is (or was) a fairly common rude dismissive remark in parts of North America.
"Tough titmouse" is thus somewhat similar to the expression "tough snot"—which is a poorly disguised euphemism for the cruder but equally dismissive "tough shit." (In Texas in the 1960s, "tough snot" was fairly popular among English speakers in the 10-to-13-year-old cohort: it was rude enough to please a sixth-grader dismissing a peer's concerns or objections, without incurring the full wrath of any adult who might overhear.) The main difference is that "tough titmouse" is a bit cleverer because of its play on "tufted titmouse," a chickadee-like bird that lives in much the eastern half of the United States (and a bit of southeastern Canada).
Dianne Porter, a blogger at birdwatching.com posted an item called "Tough Titmouse" back in 2006, but her post seems to have nothing to do with the euphemism used in The Good Doctor. Instead, it focuses on the persistent aggressive behavior of a male tufted titmouse that lived near her house and spent months challenging mirror images of itself in her house's windows and her car's side mirrors and chrome trim. The wordplay here seems limited to tough and tufted.
A Google search turns up very few published instances of "tough titmouse," including just one in a book—in Kieran Crowley, Shoot: An F.X. Shepherd Novel (2016)—where it appears to rather ludicrous effect:
I have no doubt that "tough titmouse" as a euphemism has some following in North America and may go back decades in some areas, but there is nothing more to it than the convenient similarity of the words to something naughtier—not unlike "particularly nasty weather" in the old joke.