Short answers, pulled from the story.
Panentheism is the belief that the divine intersects every part of the universe and also extends beyond space and time. Pantheism holds that the divine and the universe are identical, while panentheism maintains an ontological distinction between the divine and the non-divine, insisting that God contains the universe but is greater than it.
The German philosopher Karl Christian Friedrich Krause, who lived from 1781 to 1832, coined the term panentheism in 1828. He derived it from the Ancient Greek expression meaning "all in god" and used it to distinguish the philosophies of Hegel and Schelling from what he saw as the pantheism of Baruch Spinoza.
Several major schools of Hindu thought are regarded as panentheistic, including Nimbarka's Dvaitadvaita, Ramanuja's Vishistadvaita, Saiva Siddhanta, Kashmir Shaivism, Chaitanya Mahaprabhu's Gaudiya Vaishnavism, and Shaktism. The Bhagavad Gita expresses a panentheistic view in verse IX.4, where Krishna states that all beings abide in him, though he does not abide in them.
Charles Hartshorne, who lived from 1897 to 2000, popularized the term panentheism and developed it through process theology. He formulated God as a being capable of becoming more perfect, holding absolute perfection where it is possible and relative perfection in categories where it cannot be precisely determined. He also reviewed and discarded pantheism, deism, and pandeism in favor of panentheism.
Yes, panentheism appears within Jewish mystical traditions. The Kabbalah scholar Moshe Idel traces the doctrine to Moses ben Jacob Cordovero (1522-1570), and in the eighteenth century to the Baal Shem Tov (c. 1700-1760), founder of the Hasidic movement. Hasidism holds that the infinite Ein Sof exists in a state that is both transcendent and immanent, a core panentheistic position.
The Purusha Sukta, found in the later section of the Rig Veda and compiled before 1100 BCE, is considered the earliest reference to panentheistic thought in Hindu philosophy. It describes Purusha, the cosmic being, as both immanent in the manifested world and transcendent to it, with the original creative will projecting the universe across space and time.