c. 1300, "fixed payment (usually in exchange for taxes collected, etc.), fixed rent," from Old French ferme "a rent, lease" (13c.), from Medieval Latin firma "fixed payment," from Latin firmare "to fix, settle, confirm, strengthen," from firmus "strong; stable," figuratively "constant, trusty" (from suffixed form of PIE root *dher- "to hold firmly, support").
Sense of "tract of leased land" is first recorded early 14c.; that of "cultivated land" (leased or not) is 1520s. A word of confused history, but there is agreement that "the purely agricultural sense is comparatively modern" [Century Dictionary]. There is a set of Old English words that appear to be related in sound and sense; if these, too, are from Latin it would be a very early borrowing. Some books strenuously defend a theory that the Anglo-Saxon words are original (perhaps related to feorh "life").
Phrase buy the farm "die in battle," is from at least World War II, perhaps a cynical reference to the draftee's dream of getting out of the war and going home, in many cases to a peaceful farmstead. The simple term buy it as slang for "suffer a mishap," especially "to die" is attested by 1825, and seems to have been picked up in airmen's jargon. Meanwhile fetch the farm is prisoner slang from at least 1879 for "get sent to the infirmary," with reference to the better diet and lighter duties there.
mid-13c., "property" of any kind, including money, land, income; from Anglo-French catel "property" (Old North French catel, Old French chatel), from Medieval Latin capitale "property, stock," noun use of neuter of Latin adjective capitalis "principal, chief," literally "of the head," from caput (genitive capitis) "head" (from PIE root *kaput- "head"). Compare sense development of fee, pecuniary.
in later Middle English especially "movable property, livestock" (early 14c.), including horses, sheep, asses, etc.; it began to be limited to "cows and bulls" from late 16c.
1610s, "country mansion of the ancient Romans," from Italian villa "country house, villa, farm," from Latin villa "country house, farm," related to vicus "village, group of houses," from PIE *weik-sla-, suffixed form of root *weik- (1) "clan." Of modern structures from 1711.