mid-15c., "lacking form; not in accordance with the rules of formal logic," from in- (1) "not, opposite of" + formal (adj.). Meaning "irregular, unofficial, not according to rule or custom" is from c. 1600. Sense of "done without ceremony" is from 1828. Related: Informally.
-ity
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]