Certainly not. His genesis is explicitly described in the episode and while it's possible that he had something to do with the Q (heck, anything is possible when Q is involved) it's vanishingly unlikely.
TROI: Abandoned. Who deserted you?
ARMUS [OC]: Creatures whose beauty now dazzles all who see them. They would not exist without me.
TROI: You were together?
ARMUS [OC]: They perfected a means of bringing to the surface all that was evil and negative within. Erupting, spreading, connecting. In time it formed second skin, dank and vile
Frankly, no part of that description matches what we know about the Q.
Almost certainly not. Although he possesses many of the overt powers of the Q (the ability to manifest unreal objects, for example), his actions don't teach the crew anything. There's no "lesson learned", a common feature of all of the Q's interactions with humanity. He also seems rampantly (and needlessly) cruel, rather than possessing any of the vicious charm of Q. Frankly, murdering a junior crewman simply to make a point just isn't Q's style.
Nagilum: ... Be that as it may -- as species, we have no common ground. You are too aggressive. Too hostile. Too militant. - Where Silence Has Lease
Q: The Q became interested in you. Does no one here understand your incredible good fortune? - Hide and Q