Why for a dipole antenna half wave length is optimum size?
A couple things.  First, a center fed dipole antenna that is slightly shorter than half wave length is in resonance, which means its impedance is purely resistive.  Typically, its impedance is about 70 ohms.

I think by transmission line resistance you mean impedance.  You can make transmission lines with impedances lower than 50 ohms, but these are not common.  Most coaxial cable is either 50 of 75 ohms, with 75 ohm being less lossy for a given diameter.