The purpose of this paper is to continue the study initiated in [7] concerning the notion of pseudo-generalized inverse. In this work, we are interested in investigating the relationship between compactness, finite rank and pseudo-generalized invertibility for bounded operators. The preserving properties of products of pseudo-generalized invertible operators are also treated and related results are given. At the end of this paper, we discuss in some special cases the relationship between the sets of n-left pseudo-generalized inverses of a left pseudo-generalized invertible operator T.