A modified theory of gravity, avoiding singularities in the standard theory of gravitation, has been developed by Hess & Greiner, known as pseudo-complex theory of gravitation. The pc-GR theory shows remarkable observational differences with respect to standard GR. The intensity profiles are remarkably different between both theories, which is a rare phenomenon in astrophysics. This will allow robust tests of both theories by using Event Horizon Telescope (EHT) observations of the Galactic Center. We also predict the time evolution of orbiting matter. In this paper we summarize the observational tests we have developed to date. The theory is described in the second paper of this series (Hess et al. 2019, refereed to as paper II hereafter).