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2 powered raspberry pis and a moderately functioning internet is the answer.

The network adjusts it's requirement for power based on the total power thrown at it. This is called "difficulty adjustment". Beyond total world collapse that would set society back a century, I cannot imagine a scenario where you couldn't continue running Bitcoin as long as a few people had the motivation.

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If they had the motivation, yes. However, why would the have the motivation instead of simply using well-known limited physical currencies, such as cigarettes, gold etc? Especially since you'd need to make the money using power and if power is sparse, you'd probably need the bit you get for refrigeration or cooking.

Solar flare?

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