Question

To which band does the Fermi level belong - valence band or conduction band?

Answer 1

In metals and semimetals the Fermi level EF lies inside at least one band. Ininsulators and semiconductors the Fermi levelis inside a band gap; however, in semiconductors the bands are near enough to the Fermi level to be thermally populated with electrons or holes.
It doesn't belong to conduction or valence band ; the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In non-metals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.