Dear ensabah, nope, the existence of a 6-dimensional manifold at each point of the 3+1-dimensional space doesn't imply any discreteness.
In topological string theory, the sizes of the hidden manifold are quantized. In the full physical string theory, they can't be. Everything is continuous. With a B-field, one can get a noncommutativity on the hidden manifold which effectively makes the space of functions on the manifold finite-dimensional, as expected from N points. This is the closest point to a "discreteness" but you can never imagine that they're real "points" and the manifold is made out of edges, triangles, or simplices.
I don't understand why you think that there's a contradiction between the existence of a Calabi-Yau space and the continuity of space. There's no contradiction. The Calabi-Yau manifolds are perfectly smooth and dividable to arbitrarily small pieces, too.
Below the fundamental scale, the usual geometric intuition breaks down. But it is surely not replaced by an even more naive intuition, such as a space constructed of edges and triangles. The physics that replaces the usual long-distance physics is much more subtle and requires somewhat complicated mathematics that is not equivalent to any simple presentation for the laymen.
Neither SUSY breaking nor any moduli stabilization or any other process that is essential in the KKLT or other famous groups of stringy vacua breaks the Lorentz invariance at the fundamental scale. The Lorentz invariance at the fundamental scale is a universal principle valid according to string theory. All symmetry breaking mechanisms for similar symmetries are cases of spontaneous symmetry breaking in string theory: it means that the symmetry holds at high energies (short distances) and is being broken at low energies (long distances), below the symmetry-breaking scale.
Analogously, moduli are "massless at high energies", meaning that the masses are negligible relatively to these high scales, but they do acquire small potentials and masses that matter for long-distance physics. Also, supersymmetry breaking splits the supermultiplets, making the unknown superpartners heavier than their observed counterparts. But these mass differences are small relatively to the Planck scale which means that at short distances, when we care about big energies only, SUSY is restored. The same principle applies to electroweak, GUT, or any other similar symmetry breaking.
In the LQG and similar discussions of Lorentz symmetry, the opposite direction of the symmetry breaking is assumed: the symmetry shouldn't exist at high energies but it should be restored at low energies. This is infinitely unlikely because the short-distance physics is fundamental, and the long-distance physics is its consequence. You can say that long-distance physics may be calculated from - i.e. evolves from - short-distance physics. This evolution is analogous to the evolution in time, and restoration of symmetry is analogous to a low-entropy state. In thermodynamics, low-entropy states don't normally evolve from generic high-entropy states in the past. In the very same way, symmetric effective long-distance laws of physics usually don't evolve from asymmetric short-distance laws unless there is a reason to expect that the symmetric point is an attractor, which is not the case for Lorentz symmetry of realistic effective theories.