  Three $q$-Painlev\'e type equations are derived through degenerations of the
$q$-Painlev\'e equation with affine Weyl group symmetry of type
$q$-$E_8^{(1)}$. The three $q$-Painlev\'e type equations are associated with
different realizations of the same symmetry/surface type
$q$-$E_7^{(1)}$/$q$-$A_1^{(1)}$. We give three representations of affine Weyl
group actions of type $q$-$E_7^{(1)}$, and relations among them. The three
$q$-$E_7^{(1)}$ equations are also derived from the three representations
respectively.
