What I'd also like to know is why a cluster of gas stations ends up with different prices.

Same reason there are different buy/sell positions on the stock market. People have all kinds of different strategies and portfolios and the price at any given time represents a snapshot of these fluctuating values. Not everyone buys gas for the same price at the same time, not everyone is shooting for the same margin, some may use gas as a loss leader to encourage purchase of overpriced goods in the accompanying store, etc.