Well pretty much exactly what my title says. I'm scared I might sound crazy if I go too into it I guess, so for right now can anyone please help tell me if coins ever get printed on much much older or even different kinds of coins? Plus it's not like I could take a picture anyways if I wanted because it's terribly tough to see
The easiest answer is no. Sometimes coins are overstruck on other coins, but usually only a year or two before. You mention a 1974 quarter, which means it was struck on a clad planchet. The mint did not officially begin using clad planchets until 1965, so it wouldn't make sense for a 1974 quarter to be struck over any coin minted 1964 and earlier, as those would've been 90% silver. Also, if it was struck over anything other than a quarter size, than the coin would either be very much warped and thing, as the diameter and thus collar for a quarter is much larger than a dime, cent or nickel. I hope that explanation was helpful, if you have more questions, ask away.
Other countries have overstruck coins on earlier coins, but it is not something that has happened very much at the US Mint. (It does happen, but not very often.) And usually the host coin (the undertype) is not "much, much" older, but relatively close (within 20 years or so, and usually less) to the new, overstruck type. Here is a 1795 copper 5-reis coin from the Portuguese Azores which was overstruck on an earlier coin (a 1776 3-reis piece, in this case). You can see traces of the original host coin (the undertype). This is usually the case with overstruck pieces. Some ghostly details of the undertype will appear. See all the weird little things going on, here, and how weird the lettering and other features look?
Actually, it happens quite often, but never legitimately. Surprisingly, they sell for thousands. I never understood it.
Despite you obvious skepticism, there are plenty out there. Jon Sullivan sold this 2000 Nickel on 1961 Cent for $9,000. There are other examples in his archives. Heritage has sold some, as has Fred Weinberg.
Sorry to beat a dead horse, and please correct me if I'm wrong, but kindly tell me how this could happen other than a U.S. Mint employee messing with the equipment?
I can think of no other way. The answer to the OPs question remains “yes”. PS I’ve heard speculation this can happen when a visitor decides to get funny. Again, I don’t know.