We obtain two new MPC parameterized algorithms for DAGs running in time $O(k^2|V|\log(|V|) + |E|)$ and $O(k^3|V| + |E|)$. We also obtain a parallel algorithm running in $O(k^2|V| + |E|)$ parallel steps and using $O(\log(|V|))$ processors (in the PRAM model). We also obtain edge sparsification algorithms preserving the width of the DAG with the same running time as our MPC algorithms.