Importance of supersingularity of elliptic curves
Your questions are a bit too rambly, so I'll just answer the title question. We use supersingular curves because ordinary curves don't have enough isogenies. Specifically, for supersingular curves, the graph of $\ell$-isogenies defined over $\mathbb{F}_{p^2}$ has good expansion properties. For ordinary curves, the graph of $\ell$-isogenies does not have good expansion properties. In most cases the latter graph is just a union of disjoint cycles. You can get graphs of ordinary isogenies with good expansion properties, but in order to do so you have to do something like take the union of $\ell$-isogeny graphs over various different $\ell$.