Question about hash collisions
The general idea is that either one of the inner hashes, or the combining hash must collide, since there is not other place to introduce the collision.

Assume we found a collision for H. This means we have X, Y with $X \neq Y$ such that:

$h(h(X_0)||h(X_1)) = h(h(Y_0)||h(Y_1))$

Now we define: $A = h(X_0)||h(X_1)$ and $B = h(Y_0)||h(Y_1)$

This gives us a new equation h(A) = h(B)


If $A \neq B$, we found a collision, and are done.
If $A=B$ we know that $h(X_0)||h(X_1) = h(Y_0)||h(Y_1)$, which we can split into $h(X_0)=h(Y_0) \land h(X_1)=h(Y_1)$. From $X \neq Y$ follows $X_0 \neq Y_0 \lor X_1 \neq Y_1$. Thus at least one of $h(X_0)=h(Y_0)$ and $h(X_1)=h(Y_1)$ has different inputs on both sides of the equation, and thus represents a collision.