Short answers, pulled from the story.
The Theravada Kathāvatthu text contains early rules on debate and reasoning possibly dating back to the time of Ashoka around 240 BC. This text discusses proper methods for critical discussions on doctrine through structured dialogues called vadayutti.
Dignaga defended only two valid means of knowledge: perception and inference. He argued that perception acquires information through the senses without susceptibility to error though interpretation processes remain open to mistakes.
Dharmakirti introduced the idea that valid cognition must confirm causal efficacy by complying with an object's capacity to perform functions. His work established him as a primary theorist of Buddhist atomism alongside Dignaga.
Hindu philosophers from Nyaya Vaiseshika and Vedanta schools debated constantly against Buddhist nominalism. Uddyotakara and Prashastapada critiqued Dignaga's views while developing their own realist positions.
Sakya Pandita secured place of Dharmakirti's Pramānavārttika as foundational text on epistemology in Tibet during the thirteenth century. His work Tshad-ma rigs-gter Treasury of Logic on Valid Cognition became cornerstone of modern monastic education.