This is the first of a series of papers devoted to the topology of symplectic Calabi-Yau 4-manifolds endowed with certain symplectic finite group actions. We completely determine the fixed-point set structure of a finite cyclic action on a symplectic Calabi-Yau 4-manifold with \(b_1>0\). As an outcome of this fixed-point set analysis, the 4-manifold is shown to be a \(T^2\)-bundle over \(T^2\) in some circumstances, e.g., in the case where the group action is an involution which fixes a 2-dimensional surface in the 4-manifold. Our project on symplectic Calabi-Yau 4-manifolds is based on an analysis of the existence and classification of disjoint embeddings of certain configurations of symplectic surfaces in a rational 4-manifold. This paper lays the ground work for such an analysis at the homological level. Some other result which is of independent interest, concerning the maximal number of disjointly embedded symplectic (-2)-spheres in a rational 4-manifold, is also obtained.