In a semiconductor, the number of charges is determined by the density of impurities. Exceptions at high temperature or if the gap is very small, and then temperature may suffice to put electrons in the conduction band and holes in the valence band.

No understandable reason for conductivity trends.

Effective mass can't be inferred from simple values like atomic number. It depends on the detailed shape of the bands.

Example: diamond, silicon, germanium have the same valence and crystal shape but different conduction bands, with minimums in the 111 directions for Ge and 110 for Si, resulting from underlying orbitals. Since the effective mass depends on the band's curvature around the minimum, 111 being lower in Ge prevents any comparison with Si, where 110 is lower than 111.

Example: GaAs has the same crystal shape and size as Ge precisely, and the same atomic number as a mean value, but ion charges on Ga and As prevent the minimums in the 111 directions, so the minimum in the conduction band is at 0 for GaAs. Hence no comparison possible with Ge.

Effective mass: it's a relation between the electron's energy E and its moment p=h*k/2pi where k is the number of radians per metre ("wave number") of the electron's wave function. m is defined by E=p^{2}/2m as anywhere. It is a dispersion relation.