cockpit n.

"male of the domestic fowl," from Old English cocc "male bird," Old French coc (12c., Modern French coq), Old Norse kokkr, all of echoic origin. Compare Albanian kokosh "cock," Greek kikkos, Sanskrit kukkuta, Malay kukuk. "Though at home in English and French, not the general name either in Teutonic or Romanic; the latter has derivatives of L. gallus, the former of OTeut. *hanon-" [OED]; compare hen.

Old English cocc was a nickname for "one who strutted like a cock," thus a common term in the Middle Ages for a pert boy, used of scullions, apprentices, servants, etc. It became a general term for "fellow, man, chap," especially in old cock (1630s). A common personal name till c. 1500, it was affixed to Christian names as a pet diminutive, as in Wilcox, Hitchcock, etc.

A cocker spaniel (1823) was trained to start woodcocks. Cock of the walk "overbearing fellow, head of a group by overcoming opponents" is from 1855 (cock in this sense is from 1540s). Cock-and-bull in reference to a fictitious narrative sold as true is first recorded 1620s, perhaps an allusion to Aesop's fables, with their incredible talking animals, or to a particular story, now forgotten. French has parallel expression coq-à-l'âne.

Cock-lobster "male lobster" is attested by 1757.

The cock-lobster is known by the narrow back-part of his tail; the two uppermost fins within his tail are stiff and hard, but those of the hen are soft, and the tail broader. The male, though generally smaller than the female, has the highest flavour in the body; his flesh is firmer, and the colour, when boiled, is redder. [Mrs. Charlotte Mason, "The Ladies' Assistant for Regulating and Supplying the Table," London, 1787]

Old English pytt (Kentish *pet), "natural or man-made depression in the ground, water hole, well; grave," from Proto-Germanic *putt- "pool, puddle" (source also of Old Frisian pet, Old Saxon putti, Old Norse pyttr, Middle Dutch putte, Dutch put, Old High German pfuzza, German Pfütze "pool, puddle"), an early borrowing from Latin puteus "well, pit, shaft."

The Latin word is perhaps from PIE root *pau- (2) "to cut, strike, stamp," but there are phonetic and sense objections.

Short u makes it impossible to directly derive puteus from paviō 'to strike'. It might be related to putāre 'to prune', but this is semantically less attractive, and the suffix -eus can then hardly be interpreted as indicating a material. Therefore, puteus may well be a loanword. [de Vaan]

Meaning "abode of evil spirits, hell" is attested from late 12c.  Meaning "very small depression or dent in the surface of an object" is from early 15c. The anatomical sense of "natural depression or hollow in some part of the body" is by late 13c,; the pit of the stomach (1650s) is so called from the slight depression there between the ribs; earlier words for it were breast-pit (late 14c.), heart-pit (c. 1300).

The meaning "part of a theater on the floor of the house, lower than the stage," is from 1640s; the sense of "that part of the floor of an exchange where business is carried on" is by 1903, American English. The pit dug under a large engine or other piece of machinery to allow workers to examine or repair it is attested by 1839; this later was extended in auto racing to "area at the side of a track where cars are serviced and repaired" (by 1912).