For question d part i, I have calculated the distances from $Q$ to $P_1$ and $P_2$ respectively and found $P_1$ to be closer with a distance of root $6$, with $P_2$ having a distance of root $24$.
However, I am not sure how to begin/answer d part ii. Any help would be appreciated.
If a plane in $\mathbb{R}^3$ has normal vector $n$, the two regions into which it divides $\mathbb{R}^3$ are $\{X\in \mathbb{R}^3: \langle X,n\rangle > 0\}$ and $\{X\in \mathbb{R}^3: \langle X,n\rangle < 0\}$. In the above question, $P_i$ will be visible to $Q$ if and only if $P_i$ and $Q$ lie in the same one of these two regions, so you just need to know the signs of $\langle P_1,n\rangle$,$\langle P_2,n\rangle$,and $\langle Q,n\rangle$ to figure this out.