Strictly speaking, the angle does not have to be within $0$ and $\pi$. But to find the angle between these two vectors, you would use the $\arccos$ function, and the usual $\arccos$ function has restricted domain and range: $[-1,1]$ and $[0, \pi]$. Moreover, suppose we got an angle of, say $3\pi/4$. Then we can also view the angle between the two vectors as $\pi/4$ by tilting our heads a bit.
The vectors don't have to be in standard position for measuring the angle between them to work. But if you want to have a picture in mind for the concept, then it would be that you put the tails of the two vectors together, then measure the angle between them. You can think of where the tails meet as the origin, just for convenience. But there's nothing special about the origin when it comes to the dot product.
Except this last part about orthogonality, I guess. The question isn't "why is that so," because the definition of orthogonality is that two vectors $\mathbf{u}$ and $\mathbf{v}$ are orthogonal if and only if $\mathbf{u}\cdot\mathbf{v}=0$. The zero vector satisfies $0\cdot\mathbf{v}=0$ for every vector $\mathbf{v}$ (just write out the dot product coordinatewise to see), so by definition it is orthogonal to every vector.