Polar form of eigenvalue
I think all it's saying is that we can write $H(\Omega)$ as:

$$
H(\Omega) = \left| H(\Omega) \right | e^{j \angle H(\Omega) }
$$

It also seems to be assuming that $h(t)$ is real-valued so that $H(-\Omega) = H^*(\Omega)$.

The function $H(\Omega)$ is just a map from $\mathbf{R} \mapsto \mathbf{C}$ (from the reals to the complex numbers).  For any specific value of $\Omega$ this generates a single complex number $H(\Omega)$. And, as you say, any complex number resolves to its exponential notation.