Note that the genetics of man agrees that woman came from out of man.
And here for the last 62.7 years I've been carrying around these pitiful little Y chromosomes which look like a faint shadow of the X chromosomes that came first. "Man" was derived from "woman" here in the clade Mammalia.
Genesis flunks Biology 101 yet again.
And thus we see that the woman was created at the same moment God created man but not yet given a bodily form.
Not if you read the text you just quoted. Wouldn't it be the "plain reading" that Adam had to be awake to be put into a "deep sleep?"