Short answers, pulled from the story.
Hero of Alexandria published schematics for a steam engine that rotated a ball on a pivot using heat from a cauldron. The machine produced roughly 1500 rpm but never became practical for industrial use due to high labor costs.
The Pantheon dome utilized Roman concrete mixed with lime and volcanic powder called pozzolana to form a substance as hard as natural rock. This mortar could form underwater and provided increased tensile strength compared to pure lime mixtures without requiring complete drying to cure.
Eleven aqueducts made of limestone supplied Rome with over one million cubic meters of water daily, including the Aqua Claudia and Aqua Marcia. These systems relied entirely on gravity to transport water through raised stone channels from mountain springs to collection tanks.
The pilum javelin weighed approximately five pounds or 2.25 kilograms and was designed for single use only. Legionaries carried two versions consisting of a primary spear and backup weapon while solid wood blocks protected hands during carrying.
More than 400,000 kilometers of roads were constructed across the empire with significant portions paved using layers of rocks gravel sand concrete and polygonal rock slabs. Bridges built over waterways utilized stone and concrete arches such as the Alcántara Bridge constructed between 104 and 106 CE.