We study noncentrosymmetric superconductors with the tetrahedral $T_d$, tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed self-consistently in the bulk and near a surface for several different singlet to triplet order parameter ratios. It is shown that a second phase transition below $T_c$ is possible for certain parameter values. In order to determine the surface orientations effect on the order parameter suppression, the latter is calculated for a range of different surface orientations. For selected self-consistent order parameter profiles the surface density of states is calculated showing intricate structure of the Andreev bound states (ABS) as well as spin polarization. The topologys effect on the surface states and the tunnel conductance is thoroughly investigated, and a topological phase diagram is constructed for open and closed Fermi surfaces showing a sharp transition between the two for the cubic point group $O$.
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