For the minimum question, this is answered in Theorem 4 of 
<cite authors="Erdős, Paul; Füredi, Zoltán; Tuza, Zsolt">_Erdős, Paul; Füredi, Zoltán; Tuza, Zsolt_, [**Saturated \(r\)-uniform hypergraphs**](http://dx.doi.org/10.1016/0012-365X(91)90035-Z), Discrete Math. 98, No. 2, 95-104 (1991). [ZBL0766.05060](https://zbmath.org/?q=an:0766.05060).</cite>

The answer is $\frac{n^2}{k(k-1)^2}+\Theta(n)$, and you can get something a bit more precise from their proof if you need.