1705, "phase of the moon, particular recurrent appearance presented by the moon (or Mercury or Venus) at a particular time," back-formed as a singular from Modern Latin phases, plural of phasis, from Greek phasis "appearance" (of a star), "phase" (of the moon), from stem of phainein "to show, to make appear" (from PIE root *bha- (1) "to shine").
Latin singular phasis was used in English from 1660 for each of the aspects of the moon. General (non-lunar) sense of "aspect, appearance, stage of development at a particular time" is attested by 1841. Meaning "temporary difficult period" (especially in reference to adolescents) is attested from 1913.
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.