  We define Kazhdan-Lusztig bases and study asymptotic forms for affine
$q$-Schur algebras following Du and McGerty. We will show that the analogues of
Lusztig's conjectures for Hecke algebras with unequal parameters hold for
affine $q$-Schur algebras. We will also show that the affine $q$-Schur algebra
$\mathcal{S}_{q,k}^{\vartriangle}(2,2)$ over a field $k$ has finite global
dimension when char $k=0$ and $1+q\neq 0.$
