Does Resistivity increases with increase in temperature,  and decreases with decrease in temperature?

Yes, it does. In the metal, the atoms are in state of vibrating motion when the temperature increases, the amplitude of vibration will increases more and also increases the speed of the carriers of current i.e. electrons. In this process, free electrons collide with ions while drifting towards the positive end of the conductor more often which decreases the relaxation time. Hence, electrical resistivity of conductor  increases with increase in temperature and decreases with decrease in temperature.