Universe structure emerges in the unreduced, complex-dynamical interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis avoiding any perturbative model gives intrinsically creative cosmology describing the real, explicitly emerging world structure with dynamic randomness at all levels. Without imposing any postulates or additional entities, we obtain physically real, three-dimensional space, irreversibly flowing time, elementary particles with their detailed structure and intrinsic properties, causally complete and unified version of quantum and relativistic behaviour, the origin and number of naturally unified fundamental forces, classical behaviour emergence in a closed system, and true quantum chaos. Major problems of standard cosmology and astrophysics are consistently solved in this extended picture, including those of quantum cosmology and gravity, entropy growth and time arrow, "hierarchy" of elementary particles (Planckian unit values), "anthropic" difficulties, Big Bang contradictions, and "missing" ("dark") mass and energy. Universality of the proposed theory is explicitly expressed by the symmetry (conservation and transformation) of dynamic complexity providing the unified, irregularly structured, but always exact (never "broken") Order of the World that underlies all universe structures, phenomena and laws.