Thanks for your question Harry, I think I can answer it.
First off, the Planck time (around 10-44 sec) is the moment at which a particle's Compton wavelength (the scale at which quantum effects become important) becomes equivalent to the particle's Schwarzschild radius (the scale at which gravity becomes important). Therefore, it defines this moment when two important kinds of physics are both relevant, namely, quantum theory and general relativity. There is currently no known theory that successfully incorporates both quantum theory and general relativity, and so that's why you might hear people say that the "laws of physics do not apply here." However, it is widely believed that some theory applies here, it has just yet to be found.
However, current physical theories are capable of describing the universe after the Planck time. These theories are consistent with a universe in which 3 of the fundamental forces (electromagnetic, strong & weak nuclear) were unified into a single "superforce". It is conjectured that if we were to rewind the tape all the way back to the Planck time, gravity would join this "superforce" (and I suppose make it a super-superforce). However, whether this does (or even should) occur is not known.
Lastly -- your question about the expansion. Since we don't know the physics of the Planck era, we don't know how the universe was behaving -- we have no idea if it was expanding, contracting, or just sitting idly. However, after the Planck time, the universe was expanding. At this time, Einstein's special relativity is certainly applicable, and so we expect all particles to obey the speed limit v < c. Particles can't move a light year per second, so perhaps there was more to that story. What can happen, is that two particles can have relative velocities that surpass that of light.This is of course still troubling from the perspective of special relativity. However, everything is OK, and here's why: the particles themselves are at rest in space -- it is the space itself that is expanding, causing these particles to separate. There are no rules limiting the speed at which space itself can expand. In cosmology, we often see particles zipping apart from each other at speeds greater than that of light.