Wouldn't a nationwide bank run result in hyperinflation?
A bank run is an increase in demand for currency. Which would create hyperdeflation, as the value of currency rose to meet the clearing price at the current supply.
I don't follow you. If you will, please break it down.
All of those accounts are "insured" for up to $250,000. Where will this money come from? They will have to issue more money or default on their promises.