Short answers, pulled from the story.
Metaphysics is the branch of philosophy that examines the basic structure of reality, including existence, objects and their properties, possibility and necessity, space and time, change, causation, and the relation between matter and mind. It is one of the oldest branches of philosophy and is traditionally seen as the study of mind-independent features of the world.
Aristotle designated metaphysics as the first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry. The label implies it is the most basic inquiry upon which all other branches of philosophy depend in some way.
The word metaphysics comes from the ancient Greek words metá and phusiká and entered English in the mid 1500s through the Latin word metaphysica. Aristotle did not use the term himself; an editor some two centuries later, likely Andronicus of Rhodes, coined it as the title of his book, presumably to indicate it should be studied after Aristotle's Physics.
Particulars are unique, non-repeatable individual entities, like a specific apple, the Eiffel Tower, or the number 2. Universals are general features that different particulars share, like the color red, and they are repeatable because they can be instantiated by several particulars at the same time.
A possible world is a complete and consistent way the totality of things could have been, a concept borrowed from Gottfried Wilhelm Leibniz to analyze modal statements. A statement is possibly true if it is true in at least one possible world and necessarily true if it is true in all possible worlds.
Critics argue that humans lack the cognitive capacity to access the ultimate nature of reality, a view held by empiricists like David Hume and limited further by Immanuel Kant. Logical positivists, including Rudolf Carnap, went further and claimed metaphysical statements are meaningless because they make no testable predictions about experience.
The mind-body problem is the challenge of clarifying the relation between physical and mental phenomena. Cartesian dualism treats minds and bodies as distinct substances, monists reject that split, and the hard problem of consciousness asks how physical systems like brains can produce phenomenal consciousness.