Old English fæder "he who begets a child, nearest male ancestor;" also "any lineal male ancestor; the Supreme Being," and by late Old English, "one who exercises parental care over another," from Proto-Germanic *fader (source also of Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fatar, German vater; in Gothic usually expressed by atta), from PIE *pəter- "father" (source also of Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), presumably from baby-speak sound "pa." The ending formerly was regarded as an agent-noun affix.

My heart leaps up when I behold

  A rainbow in the sky:

So was it when my life began;

So is it now I am a man;

So be it when I shall grow old,

  Or let me die!

The Child is father of the Man;

I could wish my days to be

Bound each to each by natural piety.

[Wordsworth, 1802]

The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-." Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words, perhaps reinforced in this case by Old Norse forms; spelling caught up to pronunciation in 1500s (compare mother (n.), weather (n.), hither, gather). As a title of various Church dignitaries from c. 1300; meaning "creator, inventor, author" is from mid-14c.; that of "anything that gives rise to something else" is from late 14c. As a respectful title for an older man, recorded from 1550s. Father-figure is from 1954. Fathers "leading men, elders" is from 1580s.

also Hell, Old English hel, helle, "nether world, abode of the dead, infernal regions, place of torment for the wicked after death," from Proto-Germanic *haljō "the underworld" (source also of Old Frisian helle, Old Saxon hellia, Dutch hel, Old Norse hel, German Hölle, Gothic halja "hell"). Literally "concealed place" (compare Old Norse hellir "cave, cavern"), from PIE root *kel- (1) "to cover, conceal, save."

Old Norse Hel (from Proto-Germanic *halija "one who covers up or hides something")was the name of Loki's daughter who ruled over the evil dead in Niflheim, the lowest of all worlds (nifl "mist") It might have reinforced the English word "as a transfer of a pagan concept to Christian theology and its vocabulary" [Barnhart].

In Middle English, also of the Limbus Patrum, place where the Patriarchs, Prophets, etc. awaited the Atonement. Used in the KJV for Old Testament Hebrew Sheol and New Testament Greek Hades, Gehenna. Used figuratively for "state of misery, any bad experience" at least since late 14c. As an expression of disgust, etc., first recorded 1670s.

To have hell break loose is from c. 1600. Expression hell in a handbasket is attested by 1867, in a context implying use from a few years before, and the notion of going to Heaven in a handbasket is from 1853, implying "easy passage" to the destination. Hell or high water (1874) apparently is a variation of between the devil and the deep blue sea. To wish someone would go to hell is in Shakespeare ("Merchant of Venice"). Snowball's chance in hell "no chance" is from 1931; till hell freezes over "never" is from 1832.

To do something  for the hell of it "just for fun" is from 1921. To ride hell for leather is from 1889, originally with reference to riding on horseback. Hell on wheels is from 1843 as the name of a steamboat; its general popularity dates from 1869 in reference to the temporary workers' vice-ridden towns along the U.S. transcontinental railroad. Scottish had hell-wain (1580s) "a phantom wagon seen in the sky at night."

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.