All of the oil companies start with the same gasoline blend and add their own formula of chemicals which creates a difference between the brands. Gasoline is delivered to local mixing tanks through a nationwide pipe network, so the gas you fill up on at 7-11 is likely from the same pipe as the Chevron across the street but you get the advantage of Chevron's engine cleaning agents whereas the cheaper fuel at 7-11 may have the state-minimum of everything.
Not much between the big name brands other than what additives they advertise. As for those small companies like you or the mom and pop convenience store, and the dirt cheap chains they get the gas from the bottom of the holding tanks where all the impurities lay. Those impurities will build up in your fuel filter or clog up your fuel lines eventually.
Yes, especially if you are in cold winter area. The companies reformulate their fuel during the winter months and each is a proprietary formula. I have an older vehicle and there are some companies I cannot use during the winter because my vehicle cannot handle whatever they are doing to the fuel.