This book focuses on the quantum aspects of cosmology and black holes. The former seeks cosmological entanglement footprints of Euclidean wormholes that nucleate the inflationary universe, and the latter proposes a resolution to the information paradox via the nucleation of Hawking radiation's entangled partner pairs outside an evaporating black hole. This book begins by reviewing the connection between semi-classical Hawking radiation and the flying mirror analogue gravity model, and later their extensions to experiments and possible black hole evaporation scenarios. With the Euclidean quantum gravity approach, which originally explains the emergence of the universe(s) as something from nothing, this book calls for a something to something interpretation for the release of information to the outside of a black hole. Remarkably, the investigation on entanglement across a Euclidean wormhole in this book is refutable by the observed cosmic microwave background (CMB) power spectrum, and the proposed black hole evaporation scenario also has the potential to be mimicked by the experimentally-testable flying mirror model. This book not only provides alternative insights to resolve long-standing theoretical problems, but also excellent synergy between theories and observations/experiments.