ask over vs quest

ask over is not a noun while quest is a noun.

Word	Noun	Adjective	Verb	Adverb
ask over	No	No	Yes	No
quest	Yes	No	Yes	No

As verbs, quest is a hypernym of ask over; that is, quest is a word with a broader meaning than ask over:

Other hypernyms of ask over include ask for, bespeak, call for, request.

ask over (noun)	quest (noun)
	the act of searching for something
	a search for an alternative that meets cognitive criteria

ask over (verb)	quest (verb)
invite someone to one's house	seek alms, as for religious purposes
	express the need or desire for
	bark with prolonged noises, of dogs
	search the trail of (game)
	make a search (for)