1560s, "that which purges," from purge (v.). Meaning "a purgative, an act of purging" is from 1590s. Political or social sense of "removal (from a governing body, party, army, etc.) of persons deemed undesirable" is by 1730 (in reference to Pride's Purge); modern use in reference to the Soviet Union is by 1933. The earliest sense of the word in English was "examination or interrogation in a legal court" (mid-15c.), a sense now obsolete even if the feeling persists.
early 13c., questioun, "philosophical or theological problem" (especially when phrased as an interrogative statement), early 14c. as "utterance meant to elicit an answer or discussion," also as "a difficulty, a doubt," from Anglo-French questiun, Old French question "question, difficulty, problem; legal inquest, interrogation, torture," and directly from Latin quaestionem (nominative quaestio) "a seeking, a questioning, inquiry, examining, judicial investigation," noun of action from past-participle stem of quaerere "ask, seek" (see query (v.)).
Also in Middle English "verbal contention, debate; legal proceedings, litigation, accusation." Phrase a question of meaning "a dispute about" is from early 15c.
No question "undoubtedly" is from mid-15c; no questions asked "accountability not required" is from 1879 (especially in newspaper advertisements seeking the return of something lost or stolen). To be out of the question (c. 1700) is to be not pertinent to the subject, hence "not to be considered." To be in question "under discussion or consideration" is from 1610s.
Question mark is from 1849, sometimes also question stop (1862), earlier interrogation point (1590s). The figurative sense of "something about which there is uncertainty or doubt" is from 1869.