  In this paper, we use both local and global phase-space descriptions and
averaging methods to find qualitative features of solutions for the FLRW and
Bianchi I metrics in the context of scalar field cosmologies with arbitrary
potentials and arbitrary couplings to matter. We prove new theorems and also
retrieve previous results that can be seen as corollaries of the present
results. We study the stability of the equilibrium points in a phase-space, as
well as the dynamics in the regime where the scalar field diverges. We obtain
equilibrium points that represent some solutions of cosmological interest, such
as several types of scaling solutions, a kinetic dominated solution
representing a stiff fluid, a solution dominated by an effective energy density
of geometric origin, a quintessence scalar field dominated solution, the vacuum
de Sitter solution associated to the minimum of the potential, and a
non-interacting matter dominated solution. All reveal a very rich cosmological
phenomenology. Finally, we present some examples that violate one or more
hypotheses of the Theorems proved, obtaining some counterexamples. In
particular, we incorporate small cosine-like corrections motivated by
inflationary loop-quantum cosmology, and we study the oscillatory behavior.
