How is it possible to have a plot in a "hard" historical fiction work other than one involving added fictional characters?
By turning historical events into a narrative format? I guess I'm not really sure what you're trying to get at with the question.
In "hard" historical, the plot (though I would say 'stepping stones' is probably more accurate, esp. in the ancient world) and outcomes are known, yes. So that's the what, when, where and how. The author's contribution comes at the "why". The development of personalities, the explanation of thoughts and actions that lead from Event A to Event B, Event C, and so on. Do it right, in my opinion, and history becomes the present, giving the reader the chance to experience the horrors of the black plague, etc, right along with the characters. In other words, history becomes alive and - gasp! - accessible. At least, that's always where I thought historicals were at their best.
If a person writes a short about a small segment of history (such as the reversals in SYW that aren't going to lead to new novels), is it a short story or is it a vignette? Do vignettes count as short stories especially for contests?
Short stories aren't my thing...but I don't see why they couldn't count. In my head, at least, a vignette is just that - a glimpse, and an incomplete one at that. So we may get a look at the past, but no story arc. A short story, on the other hand, has that story arc.
But I'm probably the worst person in the world to listen to on this subject.
Is the difference between "hard" historical fiction and historical romances/mysteries/etc basically that in "hard" fiction the history is most important and in the others plot is most important?
I don't think so at all. I think the difference - speaking in broad terms - is that "hard" historicals incorporate the history into the story, and that the characters often drive or are driven by actual events. Historical romances/mysteries, etc - again speaking broadly - strike me as more "period" pieces than flat-out historicals. The history, the time period, it's a setting for a costume drama. And of course, both of these buckets have huge holes in their sides through which all the numerous exceptions can flow out of .
In my view, the known history is a plot, or at the very least a frame, directing the course of events. Come to think of it, I think it may be a difference of approach, not final product. "Hard" historicals take the history first, and then "reverse-engineer" their characters to fit into that frame. I know I did as much with my characters, and came up with some very interesting - and IMO real - personalities.
The historical romance/mystery/etc starts with a time period, but then focuses on a character or characters first, fleshing out their personality, getting a feel for them, and letting their actions drive the story. Historical events may act on them, but in a haphazard way. Which I know I'm explaining poorly, but it's early.
To finish, I think the one starts with the STORY, and the other starts with the CHARACTERS, and both meet in the middle.