Minimally 2-connected graphs have vertex of degree 2, and $m \leq 2n - 4$

Question

For the first part of the question, I know I should consider the H-path construction of 2-connected graphs. It's intuitively clear that if I try to draw these H-paths in a way that avoids vertices of degree 2, I will no longer have a minimally connected graph, but how do I make this rigorous? For the second part, the assumption is that $n \geq 4$. I'm just looking for a hint here at the moment.