Academic sense "branch of knowledge" (late 14c.) was in Old French and probably was the earliest in English (it is attested in Anglo-Latin from late 12c.), on notion of "ability in knowledge" or "body of persons on whom are conferred specific professional powers." Originally each department was a faculty; the use in reference to the whole teaching staff of an entire college dates from 1767. Related: Facultative. The Latin words facultas and facilitas "were originally different forms of the same word; the latter, owing to its more obvious relationship to the adj., retained the primary sense of 'easiness', which the former had ceased to have before the classical period." [OED]
"organ of hearing," Old English eare "ear," from Proto-Germanic *auzon (source also of Old Norse eyra, Danish øre, Old Frisian are, Old Saxon ore, Middle Dutch ore, Dutch oor, Old High German ora, German Ohr, Gothic auso), from PIE *ous- "ear" (source also of Greek aus, Latin auris, Lithuanian ausis, Old Church Slavonic ucho, Old Irish au "ear," Avestan usi "the two ears").
þe harde harte of man, þat lat in godis word atte ton ere & vt atte toþir. [sermon, c. 1250]
In music, "capability to learn and reproduce by hearing," 1520s, hence play by ear (1670s). The belief that itching or burning ears means someone is talking about you is mentioned in Pliny's "Natural History" (77 C.E.). Until at least the 1880s, even some medical men still believed piercing the ear lobes improved one's eyesight. Meaning "handle of a pitcher" is mid-15c. (but compare Old English earde "having a handle"). To be wet behind the ears "naive" is from 1902, American English. Phrase walls have ears is attested from 1610s. French orielle, Spanish oreja are from Latin auricula (Medieval Latin oricula), diminutive of auris.
late 15c., "reciprocally given and received," originally of feelings, from Old French mutuel (14c.), from Latin mutuus "reciprocal, done in exchange," from PIE root *mei- (1) "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].
The meaning "common" is from 1630s. "Used in this sense loosely and improperly (but not infrequently, and by many writers of high rank), especially in the phrase a mutual friend" [Century Dictionary].
That is common which pertains equally to two or more persons or things. That is mutual which is freely interchanged: mutual love, affection, hatred. The word is sometimes incorrectly used for common: our mutual friend, a phrase of very frequent occurrence, no doubt owing to the perfectly correct 'mutual friendship.' [J.H.A. Günther, "English Synonyms Explained & Illustrated," Groningen, 1904]
Mutual Admiration Society (1851) seems to have been coined by Thoreau. Mutual fund is recorded from 1950.
The Cold War's mutual assured destruction is attested from 1966. Assured destruction was a 1962 term in U.S. military policy circles in reference to nuclear weapons as a deterrent, popularized c. 1964 by Robert McNamara, U.S. Secretary of Defense under Lyndon Johnson, e.g. statement before House Armed Services Committee, Feb. 18, 1965. The notion was "the minimum threat necessary to assure deterrence: the capability to exterminate not less than one third of the Union of Soviet Socialist Republics' (USSR) population in a retaliatory nuclear attack." [Martin Folly, "Historical Dictionary of U.S. Diplomacy During the Cold War"].
By 1964, as the Soviet Union caught up to NATO in ICBMs, the mutual was added, perhaps first by Donald Brennan, conservative defense analyst and a public critic of the policy, who also noted the acronym MAD.)