My immediate guess is "probably no" to a fair number of your questions. While there are undoubtedly at least a few card punches and readers left in the world, my immediate guess would be that it's been long enough since anybody's tried to use them that there's little certainty that they'd work even if somebody tried.
At least based on my recollection, card punches were sufficiently reliable that many of them probably still work. They're not really a lot different from typewriters, except that when the the "thing" swings forward to hit the paper, it doesn't just hit hard enough to push a ribbon against the paper -- it swings enough harder to punch a hole through.
I'm going from distant memories, but my recollection of card readers is quite different -- that they needed servicing quite frequently. In fact, when I was working on a mainframe, I seem to recall our having three card readers -- but rarely being able to use more than two at any given time. At least if memory serves, the card sorter was actually even a bit worse. In both cases, I'm pretty sure most of the problems stemmed from the mechanical parts to feed the cards into the reader proper.
I have to say, however, that in this case I see little (if anything) to gain from "doing things the old-fashioned way." I'm hard put to think of any benefit from Hollerith cards that can't be achieved much more quickly, easily, and dependably by more modern methods. I suppose (in theory) they did encourage some discipline in programming, and actually looking carefully at code before committing to running it (which, at least in my experience, was more often "overnight" than the "10 minutes" @Kevin Cline mentions).
Truthfully, however, a decent screen is a much better way to do that than Hollerith cards. When we had to do it back then, we usually got a print-out on 132-column fan-fold paper. I can't imagine trying to proof-read even a trivial program directly on the cards.
Bottom line: good luck -- but don't get your hopes too high about really learning much from this, even in the rather unlikely even that you manage to do it.