A quite general interaction process of a multi-component system is analysed by the extended effective potential method liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the many-body problem reveals the phenomenon of dynamic multivaluedness, or redundance, of emerging, incompatible system realisations and dynamic entanglement of system components within each realisation. The ensuing concept of dynamic complexity (and related intrinsic chaoticity) is absolutely universal and can be applied to the problem of (natural and artificial) intelligence and consciousness that dynamically emerge now as a high enough, properly specified levels of unreduced complexity of a suitable interaction process. Emergent consciousness can be identified with the appearance of bound, permanently localised states in the multivalued brain dynamics from strongly chaotic states of unconscious intelligence, by analogy with classical behaviour emergence from quantum states at the lowest levels of complex world dynamics. We show that the main properties of this dynamically emerging consciousness (and intelligence, at the preceding complexity level) correspond to empirically derived properties of natural consciousness and obtain causally substantiated conclusions about their artificial realisation, including the fundamentally justified paradigm of genuine machine consciousness. This rigorously defined machine consciousness is different from both natural consciousness and any mechanistic, dynamically single-valued imitation of the latter. We use then the same, truly universal concept of complexity to derive equally rigorous conclusions about mental and social implications of this complex-dynamic consciousness concept, demonstrating its critical importance for further progress of science and civilisation.