Do hydrogen sulfide and oxygen produce pure sulfur or sulfur dioxide? If both, under which circumstances does each scenario occur?
Sulfur dioxide is not a problem ; in an aquarium it will make very dilute sulfurous acid which will likely neutralize with some carbonate mineral/gravel. H2S is lethal , extended exposure at 50 ppm for a day , or short exposure at 500 ppm. On the other hand , what you smell in aquarium sand is less then 1 ppm, the sense of smell is very sensitive to H2S. There are several answers on the internet but I expect most people can smell H2S at 0.1 ppm. An aerator will have no significant affect on H2S in an aquarium. When I clean my pond , which is well aerated ,the smell of H2s is strong from decomposing leaves, etc.
Regarding the first part of your question ; Hundreds of tons a day of elemental sulfur are made ,world wide, every day by burning H2S with limited air at high temperature. By recycling and control of gas compositions the only products are elemental sulfur and water,