Good question. Photons per se didn't appear until the breaking of the electroweak symmetry, which was right about at the end of the inflationary epoch. But still there were some sorts of massless gauge bosons flitting around the universe all through inflation, that can serve as conceptual stand-ins for the photons we see nowadays (but that didn't technically exist back then).
According to the big bang theory, the separation between points A and B [in a diagram] grew from zero to 90 million light-years during a time interval of only 300,000 years. The rate of separation, therefore, was much larger than the speed of light. For a subtle reason, however, this does not violate the stricture on faster-than-light travel. The complication stems from the fact that, in general relativity, space itself is plastic, capable of bending and stretching. In the big bang theory, the space stretches as the universe expands. The restriction on velocities remains valid, in the sense that no particle can ever win a race with a light beam. Nonetheless, the distance between two particles can increase due to the stretching of the space between them, and general relativity places no restriction on how fast the stretching can occur.