1. The particle horizon consists of those points for which light which set out at t=0 (i.e. the Big Bang) is only just reaching us. Hence the scale factor was zero when this light set out, and its redshift will be infinite. (Of course, in reality there were not any galaxies at t=0!)

As time passes, light which left these galaxies after t=0 will reach us, and this will have a smaller redshift. So the redshift of a given galaxy will be seen to decrease with time.