H often sends me emails at really odd times...2am, 5am, 7am ... almost want to ask him to please only contact me between the hours of x and y
You're totally within your rights to do that. I used to send email to WAW at those times, but that's because that's when I'm at work. But she asked me not to -- because it unnerved her, as it does you -- and I was fine with that.
The other thing you can do is set the iPhone not to fetch but to only collect email manually. That way you'll control when you GET them, even if he sends them in the Dark o' Night.
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Does anyone think it is consequential in terms of his mental stability?
Does he also send them at "normal" hours? If he's just living La Vida Night Owl, that's one thing; but if he's always awake, always on -- well it wouldn't be the first time in H'wd that someone felt the need, the need for speed.... And that would most assuredly be consequential in terms of the functions of the old brain-pan.