We present important extensions of the software SeisSol based on the arbitrary high-order Discontinuous Galerkin (DG) Finite-Element method to model seismic wave propagation using non-conforming hybrid meshes for model discretization and to account for highly heterogeneous material. In these new approaches we include a point-wise integration of numerical fluxes across element interfaces for the non-conforming boundaries preserving numerical accuracy while avoiding numerical artifacts due to the mesh coupling. We apply the proposed scheme to a scenario test case of the Grenoble valley to demonstrate the methods capability. Furthermore, we present the extension to space-variable coefficients to describe material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the wave equation. The combination of the DG method with a time integration scheme based on the solution of Arbitrary accuracy DErivatives Riemann problems (ADER) still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. We confirm the accuracy of the proposed scheme a numerical experiments considering randomly heterogeneous material and compare our results to independent reference solutions. Finally, we apply the scheme to an earthquake scenario considering the effect of a sedimentary basin and compare the efficiency of the classical global time stepping technique and the local time stepping for different partitioning strategies and show results for a strong scaling test.