are there fixed context sensitive grammars which are PSPACE complete?
$\mathrm{CSL}=\mathrm{NSPACE}(O(n))$. Thus, take your favourite PSPACE-complete problem. If it is decidable in $\mathrm{NSPACE}(O(n))$ (for example, QBF is), you are done. Otherwise, introduce a polynomial amount of padding to make it so.