Short answers, pulled from the story.
Ontology is the philosophical study of being that serves as a subdiscipline of metaphysics focused on the most general features of reality. It encompasses all existence and every entity within it to articulate the basic structure of being.
Parmenides c. 515, 450 BCE is sometimes considered the founder of ontology due to his explicit discussion of being and non-being. Discussions of the essence of reality appear in the Upanishads dating from 700 BCE with speculations about the nature of being.
Particulars are unique non-repeatable entities like the person Socrates or the Taj Mahal while universals are general repeatable entities like the color green. Universals express aspects or features shared by particulars such as Mount Everest and Mount Fuji characterized by the universal mountain.
Presocratic philosophers in Greece aimed to provide rational explanations starting in the 6th century BCE. Plato 427, 347 BCE developed his theory of forms distinguishing unchangeable perfect forms from matter and Aristotle 384, 322 BCE suggested an elaborate system of categories introducing substance as primary being.
Conceptual analysis proceeds by examining component parts and necessary conditions under which a concept applies using tools like eidetic variation and the transcendental method. Naturalistic methods rely on insights from natural sciences to determine what exists while Ockham's Razor states simple theories are preferable using few basic types or fundamental entities.