shooter n.

Middle English sheten "hasten from place to place; move swiftly; thrust forward; discharge a missile, send an arrow from a bow," from Old English sceotan (class II strong verb; past tense sceat, past participle scoten), "dart forth, go swiftly and suddenly," also "discharge (a missile or weapon);" also, of a person, "go suddenly from place to place;" also transitive "send out or forth with sudden or violent motion; put forth or extend in any direction; strike with anything shot."

This is from Proto-Germanic *skeutanan (source also of Old Saxon skiotan, Old Norse skjota "to shoot with (a weapon); shoot, launch, push, shove quickly," Old Frisian skiata, Middle Dutch skieten, Dutch schieten, Old High German skiozan, German schießen), often said to be from PIE root *skeud- "to shoot, chase, throw," but Boutkan gives it no IE etymology.

The sense of "dart along" (as pain through the nerves or a meteor in the sky) is by late 13c.; that of "come forth" (as a plant) is by late 15c. As "increase rapidly, grow quickly" by 1530s (often with up (adv.)). By 1690s as "be emitted in rays or flashes" (as light is); by 1530s in weaving, "variegate by interspersing colors."

The general sports sense of "kick, hit, throw etc. toward the goal" is by 1874. In reference to pool playing, by 1926. The meaning "strive (for)" is by 1967, American English. The sense of "descend (a river) quickly" is from 1610s. The slang meaning "to inject by means of a hypodermic needle" is attested by 1914 among addicts. The meaning "to photograph" (especially a movie) is from 1890.

As an interjection, an arbitrary euphemistic alteration of shit, it is recorded by 1934.

Shoot the breeze "chat" is attested by 1938 (as shooting the breeze), perhaps originally U.S. military slang. Shoot to kill is attested from 1867. Slang shoot the cat "vomit" is from 1785.

To shoot the moon formerly meant "depart by night with ones goods to escape back rent" (c. 1823).

O, 'tis cash makes such crowds to the gin shops roam,

And 'tis cash often causes a rumpus at home ;

'Tis when short of cash people oft shoot the moon ;

And 'tis cash always keeps our pipes in tune.

Cash! cash! &c.

["The Melodist and Mirthful Olio, An Elegant Collection of the Most Popular Songs," vol. IV, London, 1829]

Shoot against the moon was used by Massinger  (1634) as a figure of an impossible attempt.

Middle English shot "a missile, arrow, dart" (senses now archaic or obsolete); "a swift movement, a gushing out," from Old English scot, sceot "a shot, a shooting, an act of shooting; that which is discharged in shooting, what is shot forth; darting, rapid motion."

This is from Proto-Germanic *skutan (source also of Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), from PIE root *skeud- "to shoot, chase, throw." The Old English noun is related to sceotan "to shoot." The meaning "discharge of a bow, missile," also is from related Old English gesceot.

The noun was extended to other projectiles (balls, bullets) by mid-15c. Especially "lead in small pellets, a small ball or pellet," a number of which are combined in one charge, which is attested by 1770 (shortened from earlier small shot, 1727).

The general sense of "an attempt to hit with a projectile" is by 1650s. Extended to sports (hockey, basketball, etc.) by 1772, originally in curling. It is attested by early 15c. as "range or distance of a missile in flight," hence "range" in general (c. 1600), as in earshot. 

Another original meaning, "payment" (perhaps literally "money thrown down") is preserved in scot-free; also see scot (n.). The notion of "throwing down" might have led to the meaning "a drink," first attested 1670s; the more precise meaning "small drink of straight liquor" is by 1928.

The sense of "hypodermic injection" is attested from 1904; the figurative phrase shot in the arm "stimulant" is by 1922. The broad meaning "a try, an attempt" is by 1756; the sense of "remark meant to wound" is by 1841. The meaning "an expert in shooting with a firearm" is from 1780; the sense of "a rocket flight" is by 1934. The camera-view sense is by 1958.

To call the shots "control events, make decisions" is American English, 1922, perhaps from sport shooting. Shot in the dark "uninformed guess, random attempt" is by 1885. Big shot "important person" is from 1861. 

By the rude bridge that arched the flood,

   Their flag to April’s breeze unfurled,

Here once the embattled farmers stood

   And fired the shot heard round the world.

[Emerson, from "Concord Hymn"]