question vs feel out

question is a noun but feel out is not a noun.

Word	Noun	Adjective	Verb	Adverb
question	Yes	No	Yes	No
feel out	No	No	Yes	No

As verbs, feel out is a hyponym of question; that is, feel out is a word with a more specific, narrower meaning than question:

Other hyponyms of question include enquire, inquire, wonder, interpellate, examine, pump, check out, sound out, debrief.

question (noun)	feel out (noun)
uncertainty about the truth or factuality or existence of something
an instance of questioning
the subject matter at issue
a formal proposal for action made to a deliberative assembly for discussion and vote
a sentence of inquiry that asks for a reply
an informal reference to a marriage proposal

question (verb)	feel out (verb)
pose a question	try to learn someone's opinions and intentions
challenge the accuracy, probity, or propriety of
place in doubt or express doubtful speculation
pose a series of questions to
conduct an interview in television, newspaper, and radio reporting