I don't entirely understand why the Solstice is considered the start of Summer, considering it literally marks the point at which the days get shorter and head towards Winter.
Well, the equinoxes and solstices just make good dividing spots for consistent astronomical events. Also, in most places the warmest weather is not seen until after the solstice due to effects like
https://en.wikipedia.org/wiki/Seasonal_lagIn the USA we culturally see summer as ranging from the end of May (Memorial Day) to the very beginning of September (Labor Day). Unless you're talking to a pedant you'd find most people in the northern hemisphere would say the seasons are
Winter:
December January February
Spring:
March April May
Summer:
June July August
Autumn:
September October November
Depends on location. Days continue to get longer until the beginning of July here.
No they don't. The solstice is the tipping point for the amount of sunlight during the day. At best you'll see the sunset time remain relatively unchanged until July but sunrise will consistently happen later. Higher latitudes get more daylight hours overall but also see more day to day variation
