Old English scitan, from Proto-Germanic *skit- (cf. North Frisian skitj, Dutch schijten, German scheissen), from PIE *skei- "to cut, split, divide, separate" (see shed (v.)). The notion is of "separation" from the body (cf. Latin excrementum, from excernere "to separate," Old English scearn "dung, muck," from scieran "to cut, shear;" see sharn). It is thus a cousin to science and conscience.
"Shit" is not an acronym. The notion that it is a recent word might be partly because it was taboo from c.1600 and rarely appeared in print (neither Shakespeare nor the KJV has it), and even in "vulgar" publications of the late 18c. it is disguised by dashes. It drew the wrath of censors as late as 1922 ("Ulysses" and "The Enormous Room"), scandalized magazine subscribers in 1957 (a Hemingway story in "Atlantic Monthly") and was omitted from some dictionaries as recently as 1970 ("Webster's New World").
Extensive slang usage; meaning "to lie, to tease" is from 1934; that of "to disrespect" is from 1903. Shite, now a jocular or slightly euphemistic and chiefly British variant of the noun, formerly a dialectal variant, reflects the vowel in the Old English verb (cf. German scheissen); the modern verb has been influenced by the noun. Shat is a humorous past tense form, not etymological, first recorded 18c. To shit bricks "be very frightened" attested by 1961. The connection between fear and involuntary defecation has generated expressions since 14c., and probably also is behind scared shitless (1936).
Old English scitte "purging, diarrhea," from source of shit (v.). Sense of "excrement" dates from 1580s (Old English had scytel, Middle English shitel for "dung, excrement"), but use for "obnoxious person" is since at least 1508; meaning "misfortune, trouble" is attested from 1937. Shit-faced "drunk" is 1960s student slang; shit list is from 1942. Up shit creek "in trouble" is from 1937 (cf. salt river). To not give a shit "not care" is from 1922. Pessimistic expression Same shit different day attested from 1997. Shitticism is Robert Frost's word for scatological writing.
The expression [the shit hits the fan] is related to, and may well derive from, an old joke. A man in a crowded bar needed to defecate but couldn't find a bathroom, so he went upstairs and used a hole in the floor. Returning, he found everyone had gone except the bartender, who was cowering behind the bar. When the man asked what had happened, the bartender replied, 'Where were you when the shit hit the fan?' [Hugh Rawson, "Wicked Words," 1989]