  We develop an effective multiorbital mean-field t-J Hamiltonian with
realistic tight-binding and exchange parameters to describe the electronic and
magnetic structures of iron-selenide based superconductors
$A_x$Fe$_{2-y}$Se$_2$ for iron vacancy doping in the range $0 \leq y \leq 0.4$.
The Fermi surface topology extracted from the spectral function of
angle-resolved photoemission spectroscopy (ARPES) experiments is adequately
accounted for by a tight-binding lattice model with random vacancy disorder.
Since introducing iron vacancies breaks the lattice periodicity of the
stochiometric compound, it greatly affects the electronic band structure. With
changing vacancy concentration the electronic band structure evolves, leading
to a reconstruction of the Fermi surface topology. For intermediate doping
levels, the realized stable electronic structure is a compromise between the
solutions for the perfect lattice with $y=0$ and the vacancy stripe-ordered
lattice with $y=0.4$, which results in a competition between vacancy random
disorder and vacancy stripe order. A multiorbital hopping model is
parameterized by fitting Fermi surface topologies to ARPES experiments, from
which we construct a mean-field t-J lattice model to study the paramagnetic and
antiferromagnetic (AFM) phases of K$_{0.8}$Fe$_{1.6}$Se$_2$. In the AFM phase
the calculated spin magnetization of the t-J model leads to a checker-board
block-spin structure in good agreement with neutron scattering experiments and
{\it ab}-{\it initio} calculations.
