Middle English chiken, from Old English cicen (plural cicenu) "young of the domestic hen, the young of any bird;" by early Middle English, "any chicken," regardless of age, from Proto-Germanic *kiukinam (source also of Middle Dutch kiekijen, Dutch kieken, Old Norse kjuklingr, Swedish kyckling, German Küken "chicken"), from root *keuk- (echoic of the bird's sound and possibly also the root of cock (n.1)) + diminutive suffixes. By regular sound changes it should have become Modern English *chichen; the reason it didn't is unknown.
Generic words for "chicken" in Indo-European tend to be extended uses of "hen" words, as hens are more numerous than cocks among domestic fowl, but occasionally they are from words for the young, as in English and in Latin (pullus).
The meaning "one who is cowardly or timorous" is from 1610s; adjectival sense of "cowardly" is at least as old as 14c. (compare hen-herte "a chicken-hearted person," mid-15c.). As the name of a game of danger to test courage, it is recorded by 1953.
Chicken-feed "paltry sum of money" is by 1897, American English slang; literal use (it is made from the from lowest quality of grain) is by 1834. Chicken lobster "small lobster," is by 1947, American English, apparently from chicken in its sense of "young." To count (one's) chickens before they hatch "anticipate too confidently the obtaining or doing of something" is from 1570s. Chicken-fried steak (1937) is a U.S. Southern recipe that batters, breads, and fries a thin strip of steak in the way fried chicken typically is made.
shit n.
Middle English shit "diarrhea," from Old English scitte "purging, diarrhea," from source of shit (v.). The general sense of "excrement" dates from 1580s (Old English had scytel, Middle English shitel for "dung, excrement;" the usual 14c. noun for natural discharges of the bodies of men or beasts seems to have been turd or filth). As an exclamation attested in print by 1920 but certainly older. Use for "obnoxious person" is by 1508; meaning "misfortune, trouble" is attested from 1937.
Shit-faced "drunk" is 1960s student slang; shit list is from 1942. Shit-hole is by 1937 as "rectum," by 1969 in reference to undesirable locations. Shitload (also shit-load) for "a great many" is by 1970. Shitticism is Robert Frost's word for scatological writing.
Up shit creek "in trouble" is by 1868 in a South Carolina context (compare the metaphoric salt river, of which it perhaps a coarse variant). Slang not give a shit "not care" is by 1922. Pessimistic expression same shit different day is attested by 1989. To get (one's) shit together "manage ones affairs" is by 1969. Emphatic shit out of luck is by 1942.
The expression when the shit hits the fan "alluding to a moment of crisis or its disastrous consequences" [OED] is attested by 1967.
The expression 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]