as calculated by gauss‘s law.??
It's not. Most magnetic materials have hysteresis and the flux exists even when the material is not energized. No voltage will be induced, if the change in the magnetic field is 0.
It isn't! Ferromagnetic materials frequently have a residual field strength and in the case of permanent magnets that can be quite high. If you mean why is the divergence of a magnetic field always zero, then that is because there are no magnetic monopoles, i.e. no points at which magnetic field lines originate. Each magnetic field line is a closed loop so there can be no closed surface penetrated by a net flux.
