Short answers, pulled from the story.
The sulfate ion consists of one sulfur atom and four oxygen atoms arranged in a tetrahedral geometry. The sulfur atom exists in the +6 oxidation state and carries a positive charge of approximately 2.45. Modern computational analysis confirms that the four single bonds model is the most accurate representation of reality.
Gilbert Lewis proposed his radical new way to visualize the connections within the sulfate ion in 1916. His theory suggested that electrons were shared in octets around each atom to create stability. This proposal laid the groundwork for later debates involving Linus Pauling regarding double bonds and d orbitals.
Green vitriol is iron(II) sulfate heptahydrate and blue vitriol is copper(II) sulfate pentahydrate. White vitriol refers to zinc sulfate heptahydrate while alum is a double sulfate. These compounds were among the first transparent crystals observed and fueled the development of the modern chemical industry.
Lead(II) sulfate is produced on both plates during the discharge cycle of a lead-acid battery. This compound stores energy in the form of chemical bonds that can be reversed when the battery is recharged. The formation of lead(II) sulfate is a reversible process that allows for the massive scale of energy storage required to start engines.
Anaerobic microorganisms known as sulfate-reducing bacteria use the reduction of sulfates as their primary energy source. These life forms include Desulfovibrio desulfuricans which couple the oxidation of organic compounds or hydrogen with the reduction of sulfate. This biological activity converts the sulfate ion into hydrogen sulfide and other byproducts in the deep sea.
Sulfate aerosols act as a global shield that reflects sunlight back into space and cools the Earth's surface. This phenomenon known as global dimming has masked the full extent of global warming for decades. The Intergovernmental Panel on Climate Change included estimates of sulfate impact in its Second Assessment Report and by 2007 every major climate model could simulate the cooling effects of these aerosols.