inset n.

a Middle English merger of Old English in (prep.) "in, into, upon, on, at, among; about, during;" and Old English inne (adv.) "within, inside," from Proto-Germanic *in (source also of Old Frisian, Dutch, German, Gothic in, Old Norse i), from PIE root *en "in." The simpler form took on both senses in Middle English.

Sense distinction between in and on is from later Middle English, and nuances in use of in and at still distinguish British and American English (in school/at school). Sometimes in Middle English shortened to i.

The noun sense of "influence, access (to power or authorities)," as in have an in with, is first recorded 1929 in American English. to be in for it "certain to meet with something unpleasant" is from 1690s. To be in with "on friendly terms with" is from 1670s. Ins and outs "intricacies, complications of an action or course" is from 1660s. In-and-out (n.) "copulation" is attested from 1610s.

"act of setting; state or condition of being set" (originally of the sun or another heavenly body), mid-14c., from set (v.) or its identical past participle. Old English had set "seat," in plural "camp; stable," but OED finds it "doubtful whether this survived beyond OE." Compare set (n.1).

Disparate senses collect under this word because of the many meanings given the verb. The sense of "manner or position in which something is set" is by 1530s, hence "general movement, direction, drift, tendency, inclination" (of mind, character, policy, etc.), by 1560s.

The meaning "permanent change of shape caused by pressure; a bend, warp, kink" is by 1812; that of "action of hardening," by 1837. Hence "action or result of fixing the hair when damp so that it holds the desired style" (1933).

"Something that has been set" (1510s), hence the use in tennis, "set of six games which counts as a unit" (1570s) and set-point "state of the game at which one side or player needs only one point to win the set" (by 1928).

The theatrical meaning "scenery for an individual scene in a play, etc.," is by 1859, from the past-participle adjective. It later was extended in movie and television production to the place or area where filming takes place.

Set (n.1) and set (n.2) are not always distinguished in dictionaries; OED has them as two entries, Century Dictionary as one. The difference of opinion seems to be whether the set meaning "group, grouping" (here (n.2)) is a borrowing of the unrelated French word that sounds like the native English one, or a borrowing of the sense only, which was absorbed into the English word.