It's not copper. If genuine, a 1971 25 cent piece should be pure nickel.
You ask for theories. Here are mine. To answer your questions, in order:
1. Almost certainly, yes. It did not, however, come out of the mint looking like this. Therefore, this qualifies as "post-mint damage".
2. Acidic corrosion. Chemically, nickel behaves very similarly to stainless steel: when exposed to air, it quickly forms an invisibly thin protective oxide layer on the surface, which is resistant to further chemical attack. However, if you dunk the coin in strong acid, once the oxide layer is penetrated at certain spots, the raw metal is readily attacked by the acid. Leave it in the acid long enough and what you can end up with is a "shell" of protected, oxidized nickel around a core comprising nothing but corrosion products.
3. Environmental damage. It is not a "mint error".
4. If you wish; it's a free planet. But, given the answer I just gave to question 3, I suspect it would be a waste of money on your part.
5. No. The coin was made in 1971, not the Middle Ages, when mintmasters worked relatively unsupervised and unaccountable. The Mint has to account for all raw materials purchased, and purchasing zinc, tin or some other material not usually used in the coins of the day would show up on the books.
6. We do not know the history of this coin. We do not know when the damage took place, or exactly what happened to the coin before, during or after the incident that created the effect under discussion. It should be noted that just because a coin dated 1971 is received in change, does not mean it has been circulating constantly since 1971. It might have sat on the bookshelf of whoever created it for decades, before being cleaned out and banked or spent.
7. Get yourself some pure nickel quarters and some strong acids, and I suspect you can make as many of these as you wish. Therefore, they are not "rare".
8. Coincidence.
9. It is, as I said, a free planet, so you can send it away for analysis if you wish. But I suspect the answer will be "nickel compounds". Most nickel compounds are green or greenish-blue. Which compounds you might find depends on which acid did the damage: you might find nickel chloride, nickel phosphate, nickel carbonate, nickel nitrate, nickel sulfate... you get the idea. I do not know which acid might be best at creating this effect; I suspect sulfuric acid (battery acid) might do the trick.
10. No.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis