1) In BBT, there is no center. It was an expansion event of space time, not an explosion of stuff into space.
2) The only light we can observe is the flood of light that was liberated when atoms formed, which happened around 380,000 years from t=0. This light is the CMBR and has redshifted into the microwave band.
3) This liberated light was throughout the universe. We are only seeing the light that has been traveling towards us from that moment, thus traveling our way for 13.8 billion years. FTL not required.