question (n.) Look up question at Dictionary.com
early 13c., "philosophical or theological problem;" 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," 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.)).

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). Question mark is from 1849, sometimes also question stop (1862); figurative use is from 1869. To be out of the question (c.1700) is to be not pertinent to the subject, hence "not to be considered."
question (v.) Look up question at Dictionary.com
late 15c., from question (n.) and from Middle French questionner "ask questions, interrogate, torture" (13c.), from question (n.). Related: Questioned; questioning. Alternative questionize attested from 1847.