Short answers, pulled from the story.
The Upanishads are Sanskrit texts of the late Vedic and post-Vedic periods that form part of the foundational scriptures of Hinduism. They are the most recent addition to the Vedas and deal with meditation, philosophy, consciousness, and ontological knowledge. They document the transition from Vedic ritualism into new religious ideas centered on Atman and Brahman.
The two oldest Upanishads, the Brihadaranyaka and the Chandogya, are probably pre-Buddhist and may date to the 7th to 6th centuries BCE. Scholar Stephen Phillips places the full range of early or principal Upanishads between 800 and 300 BCE. The later group of around 95 Upanishads spans from the late 1st-millennium BCE to as late as the mid-2nd-millennium CE.
108 Upanishads are included in the Muktika canon, though more than 200 are known in total and new ones continued to be composed through the early modern era. The Muktika canon was listed in a text that predates 1656 CE. The most important group, called the mukhya or principal Upanishads, consists of the first dozen or so.
The Sanskrit term originally meant "connection" or "equivalence", but came to be understood as "sitting near a teacher," from upa meaning "by" and ni-sad meaning "sit down." Adi Shankaracharya interpreted the word to mean Atmavidya, or "knowledge of the self." Other translations include "esoteric doctrine", "secret doctrine", and "hidden connections."
Schopenhauer kept a copy of the Latin translation by his side and wrote: "In the whole world there is no study so beneficial and so elevating as that of the Upanishads. It has been the solace of my life, it will be the solace of my death." He found his own philosophy in accord with the Upanishads' teaching that the individual is a manifestation of one underlying reality.
The four Mahavakyas, or Great Sayings, used by Adi Shankara to establish Advaita Vedanta are: "Prajnanam brahma" from the Aitareya Upanishad, "Aham brahmasmi" from the Brihadaranyaka Upanishad, "Tat tvam asi" from the Chandogya Upanishad, and "Ayamatma brahma" from the Mandukya Upanishad. Each phrase asserts the identity of Atman and Brahman.