Question

Is it true that if a metal has more number of valence electrons, electrostatic shielding would become more pronounced?

Answer 1

No, its can not be true after a certain limit of valance electron.
Electrostatic shielding is the phenomenon of of blocking of the effect of external electric field on the internal contents inside a cage like structure (called Faraday cage). This phenomena works on the theory that the electric field inside the conductor is zero. So, as long as the material of the cage is of good conductor this phenomena will work.
Also, as long as valence electron increase to some extent ( say 1 to 3 in number) conductivity of these materials increases, hence electrostatic shielding increases. But after increase in further valence electron (say 4 to higher in number) conductivity of material generally decreases (due to increase in effective no. of electrons collisions which affects its movement i.e., material tend towards insulator) and hence this phenomena will not work so effectively in these materials as in conductors.