Yes. Higher prices encourage conservation and provide incentives to increase supply. They also allocate use to the highest valued users.
This doesn't work: you're applying long-term market considerations to an intrinsically short-term problem.
No. Might as well have an auction with the highest bidder getting the ice. Sure, this is America, free market, capitalism, supply and demand, what have you, but in America there's also a little something called competition. The week after Charley when everyone's ice machines are working and the demand goes back to normal, the guy's customers will remember his shoddy business practices and will buy their ice down the street. Nope, the author doesn't make his case.