Finding the output of frequency response
Unfortunately, apart from the amplitude $A$, I can't confirm that you're correct. The first thing that you can see without doing any calculations is that $f$ must be the same for input and output, because the system is linear and time-invariant, so the frequency of the complex exponential remains unchanged. Consequently, $f=1/7$. The output signal can be written as

$$\begin{align}y[n]&amp;=e^{j(2\pi n/7-\pi/2)}\cdot\left(1-e^{-j2\pi/7}\right)\\&amp;=e^{j(2\pi n/7-\pi/2)}\cdot e^{-j\pi /7}\left(e^{j\pi /7}-e^{-j\pi /7}\right)\\&amp;=e^{j(2\pi n/7-\pi/2)}\cdot e^{-j\pi /7}\cdot 2j\sin(\pi/7)\\
&amp;=2\sin(\pi/7)\cdot e^{j(2\pi n/7-\pi/7)}
\end{align}$$

So you have

$$\begin{align}A&amp;=2\sin(\pi/7)=0.8678\\
f&amp;=1/7=0.1429\\
\phi&amp;=-\pi/7=-0.4488
\end{align}$$