Short answers, pulled from the story.
Ancient Greeks understood that mirrors could concentrate heat rays to start fires or damage objects as early as 423 BC. One of the first accurate mentions appears in Aristophanes's comedy The Clouds written in 423 BC.
Archimedes is purported to have developed mirrors to burn attacking Roman ships during the Siege of Syracuse around 213, 212 BC. No sources from that specific time confirm this story however.
Max Planck offered the microscopic theory of radiation first in 1900 calling it quantum theory. He noted energy emitted by a radiator not continuous but in form of quanta.
Human skin sudden pain second-degree burn blisters after 5 seconds at 16 kW/m2. Thermal Protective Performance test personal protective equipment requires 80 kW/m2.
Rudolf II Holy Roman Emperor performed the experiment himself in 1611. The Accademia del Cimento updated della Porta's experiment in 1660 using a thermometer invented by Ferdinand II Grand Duke of Tuscany.