It used to be the price was dependent on the current shipment of gas dropped into the tanks. I guess that is no longer the case. The price would stay the same until the next shipment if the price was different.
Nope; the price is set by both the price paid to fill the tank and the expected price to re-fill that tank.
If a station kept the price just at what it filled the underground tank they will sell out faster at lower price point and find it hard to sell the next load at a price higher than their competitors across the street.