Not crazy, but you are getting paid in experience and exposure to being in the role. If the company is good, then you'll be considered a top performing first line employee and should receive stock options at some point in the next year to recognize your contribution. Related to question 2, you should certainly list it in your accomplishments for annual review time.
What I would recommend is sitting down with your boss' boss and say something like "I'm liking the management stuff and am glad to step up and put in some extra effort to help the team out. However, I am finding it impossible to do two full-time jobs. Here's all of what I'm doing: X, Y, Z, P, D, Q. How should I prioritize these responsibilities so I'm doing the most important 3/4 items, and who should be doing the things I can't get to?"
That's not the best wording, but the idea is to focus on trade-offs and priorities. I had those conversations all the time, and as long as I was always working on the most important 40-45 hours worth of work each week, and working diligently and smartly, I never got in trouble for not doing the stuff at the bottom of the list.
It might have been better to have that trade-off/priority conversation at day 3/4, but now that has passed, I'd say it's better to have it as soon as possible. If not, you're just building resentment/frustration, and they're not adequately informed as to what's going on to be able to respond well. You should probably have asked about the duration of the assignment at the beginning as well, but it sounds like this is new stuff to you.
In an ideal world, the duration of your boss' absence would have been better announced, and their duties would have been spread around more rather than all assigned to one person (you). I think most normal management teams would look at having you fulfill the majority of your boss' role *and* trying to do your first-line job as an unreasonable amount of work without some sort of adjustment - whether in extra salary, some extra time off later, some reduction in your regular duties, some stock options or other equity at the end of the assignment, or some combination of these.
I would not talk with HR about this, nor would I talk to the plant manager unless the plant manager also happens to be your boss' boss.
(Engineer for about 17 years, team manager for about 5 years at two Fortune 500 tech companies.)