c. 1300, "enfeebled; wearied, exhausted," from Old French faint, feint "false, deceitful; sham, artificial; weak, faint, lazy, indolent, cowardly," past participle of feindre "hesitate, falter, be indolent, show weakness, avoid one's duty by pretending," from Latin fingere "to touch, handle; devise; fabricate, alter, change" (from PIE root *dheigh- "to form, build"). Also from c. 1300 as "deceitful; unreliable; false." Meaning "wanting in spirit or courage, cowardly" (a sense now mostly encountered in faint-hearted) is from early 14c. From early 15c. of actions, functions, colors, etc., "weak, feeble, poor." Meaning "producing a feeble impression upon the senses" is from 1650s.
-ish
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.
The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.