If there's no USD so that people can evaluate their cryptos against it, then people will start pricing goods & services in BTC....no need to have USD necessarily!
Not sure when you say money you're talking about paper money or digital money. If there's no electricity then there will be no credit card/debit card and bank account working at PoS and over the internet.
Solar flare will damage as much traditional networks as crypto networks. Yet crypto networks will continue to operate since it's more decentralized and distributed.
There're also cryptos such as Power Ledger that incentives you to share and trade your extra electricity with others/neighbors so in case of any outage people will have electricity.