SNR for complex valued signal and when to use SNR and when to use Eb/N0?
Question A:
For the considered system model
$$ y[n] = x[n] + w[n], $$
as already pointed out in your previous question, it holds:
$$ E\{ y[n]y[n]^* \} = E\{ (x[n]+w[n])(x[n]+w[n])^* \} \\= E\{ x[n]x[n]^* \} + E\{ x[n] \}\underbrace{E\{ w[n]^* \}}_{= 0} + \underbrace{E\{ w[n] \}}_{= 0}E\{ x[n]^* \} + E\{ w[n]w[n]^* \} \\= E\{ x[n]x[n]^* \} + E\{ w[n]w[n]^* \}.$$
As a result, your $SNR$ will always be$$ SNR = \frac{E\{ x[n]x[n]^* \}}{E\{ w[n]w[n]^*\}}. $$
So for both of your cases the $SNR$ you specify is correct. It just depends on your definition of $x[n]$ and $w[n]$.

Question B:
For your application I would recommend to use $\frac{E_b}{N_0}$, because the energy per bit depends on the modulation scheme (BPSK, QAM etc.). Therefore comparing the $BER$ in terms of $\frac{E_b}{N_0}$ will be more fair.

You can find further information:

https://en.wikipedia.org/wiki/Eb/N0

https://de.mathworks.com/help/comm/ug/awgn-channel.html

http://www.gaussianwaves.com/2008/11/relation-between-ebn0-and-snr-2/