Disabling hardware acceleration seemed to do the trick, or at least it hasn't happened recently. I still get the black screen and popup occasionally too fast to read after I click a link but before the next page loads. But the totally disabling issue with the multiple windows on one page hasn't happened since my last post when I disabled acceleration. Never happened with Chrome or Explorer.
Thanks for the recommendations to explore gpu pages and whatnot, but I really have no intrinsic interest in fixing it except that I'm looking for a better browser. I'm willing to let someone know about a problem. If the Opera folks aren't monitoring these forums and taking an active interest in resolving problems, that's their business, but it seems a bad idea not to because they have exactly zero ways to contact them directly. How they would even hear about problems I have no idea. Incidentally, my latest gripe is no way to share web pages by email. Hopefully they've got that info already given that there have been a number of posts. I'll be moving on to another PC browser because of it.