Galois theory: Gauss-Wantzel theorem, proof explanation

Question

I am using Ian Stewart Galois theory book

and it says

1. that for $A = $ primitive $p^2$ root of unity $A$ has min poly of $m(t)= 1+ t^p +.....+t^{p(p-1)}$ and so $p(p-1)$ is a power of two. why is this so?

2. if $p^k$ -sided regular polygon is constructive, then so must $p^2$ - sided regular polygon, for $k \ge 2$. why is this so?