I have been running in circles with this problem and would greatly appreciate any help.
Apply the stepping rule repeatedly to reduce the $\displaystyle X_{t}$ to lower order to get:
$\displaystyle \Delta_{m,t}=\sum_{r=t-m+1}^t u_r$
As variance is additive you should be able to complete the first part from here.
For the second part regroup the terms to express $\displaystyle \Delta^*$ in terms of $\displaystyle \Delta$'s
RonL