fast (adj.) Look up fast at Dictionary.com
Old English fæst "firmly fixed, steadfast, constant; secure; enclosed, watertight; strong, fortified," probably from Proto-Germanic *fastu- "firm, fast" (cognates: Old Frisian fest, Old Norse fastr, Dutch vast, German fest), from PIE root *past- "firm, solid" (source of Sanskrit pastyam "dwelling place").

Meaning "rapid, quick" is from 1550s, from the adverb (q.v.). Of colors, from 1650s; of clocks, from 1840. The sense of "living an unrestrained life, eager in pursuit of pleasure" (usually of women) is from 1746 (fast living is from 1745). Fast buck recorded from 1947; fast food is first attested 1951. Fast lane is by 1966; the fast track originally was in horse-racing (1934), one that permits maximum speed; figurative sense by 1960s. Fast-forward is by 1948, originally of audio tape.
fast (v.) Look up fast at Dictionary.com
"abstain from food," Old English fæstan "to fast" (as a religious duty), also "to make firm; establish, confirm, pledge," from Proto-Germanic *fasten "to hold fast, observe abstinence" (cognates: Old Frisian festia, Old High German fasten, German fasten, Old Norse fasta "abstain from food"), from the same root as fast (adj.).

The original meaning in prehistoric Germanic was "hold firmly," and the sense evolved via "have firm control of oneself," to "hold oneself to observance" (compare Gothic fastan "to keep, observe," also "to fast"). Perhaps the Germanic sense shifted through use of the native words to translate Medieval Latin observare in its sense "to fast." The verb in the sense "to make fast" continued in Middle English, but was superseded by fasten. Related: Fasted; fasting.
fast (n.) Look up fast at Dictionary.com
"act of fasting," late Old English fæsten "voluntary abstinence from food and drink or from certain kinds of food," especially, but not necessarily, as a religious duty; either from the verb in Old English or from Old Norse fasta "a fast, fasting, season for fasting," from a Proto-Germanic noun formed from the verbal root of fast (v.). In earlier Old English fæsten meant "fortress, cloister, enclosure, prison."
fast (adv.) Look up fast at Dictionary.com
Old English fæste "firmly, securely; strictly;" also, perhaps, "speedily," from Proto-Germanic *fasto (cognates: Old Saxon fasto, Old Frisian feste, Dutch vast, Old High German fasto, German fast "firmly, immovably, strongly, very"), from *fastu- (adj.) "firm, fast" (see fast (adj.)).

The meaning "quickly, swiftly, rapidly" was perhaps in Old English, certainly by c.1200, probably from or developed under influence of Old Norse fast "firmly, fast." This sense developed, apparently in Scandinavian, from that of "firmly, strongly, vigorously" (to run hard means the same as to run fast; also compare fast asleep, also compare Old Norse drekka fast "to drink hard," telja fast "to give (someone) a severe lesson"). Or perhaps from the notion of a runner who "sticks" close to whatever he is chasing (compare Old Danish fast "much, swiftly, at once, near to, almost," and sense evolution of German fix "fast, fixed; fast, quick, nimble," from Latin fixus). The expression fast by "near, close, beside" also is said to be from Scandinavian. To fast talk someone (v.) is recorded by 1946.