We pursue in this paper our study of approximations of values and $\epsilon$-saddle-point policies in dynamic zero-sum games. After extending the general theorem for approximation, we study zero-sum stochastic games with countable state space, and non-bounded immediate reward. We focus on the expected average payoff criterion. We use some tools developed in the first paper, to obtain the convergence of the values as well as the convergence of the $\epsilon$ saddle-point policies in various approximation problems. We consider several schemes of truncation of the state space (e.g. finite state approximation) and approximations of games with discount factor close to one by the game with expected average cost. We use the extension of the general Theorem for approximation to study approximations in stochastic games with complete information. We finally consider the problem of approximating the sets of policies. We obtain some general results that we apply to a pursuit evasion differential game.