How to sort using $\texttt{SQRTSORT}$ as a subroutine which sorts $\sqrt{n}$ of consecutive elements?
Hint for part (b): Consider the statistic $r(\pi) = \sum_i |i-\pi(i)|$. Running SQRTSORT can reduce $r(\pi)$ by at most $n$, while $r(n(n-1)\ldots1) = \Omega(n^2)$.

Hint for part (c): I get a running time of $O(n^2\log^{O(1)} n)$.