We have measured Bhabha scattering at cms energies of 9.4, 13, 17, 22, 27.5, 30.0, and 31.6 GeV and the reaction e+e-→μ+μ- at 9.4 GeV. The experiment covers spacelike momentum transfers up to -850 GeV2 and timelike momentum transfers up to 1,000 GeV2. We obtain good agreement with QED comparing differential cross sections (measured between 35° and 145°), acoplanarity distributions and the energy dependence (for Bhabha scattering). Defining possible modifications of QED in a model independent way we obtain stringent limits in the range of 70-200 GeV on cutoff parameters. We test to an accuracy of 5-8% the validity of some general principles of QED, such as pointlike coupling, crossing symmetry and μe-universality.