fir filter - mean delay and snr from difference equation?
I'll give you some hints to help you solve the problem by yourself. Looking at the input-output relation, you can see that the output signal is computed only from a combination of delayed input signal values, and not from delayed output signal values. So your impulse response has a finite length and the filter can be implemented by a non-recursive structure (FIR filter). Using the impulse response, you can write the input-output relation as a finite convolution sum

$$y[n]=\sum_{k=0}^{N-1}x[n-k]h[k]\tag{1}$$

Comparing (1) to your difference equation, you can easily see what the system's impulse response $h[n]$ is. Once you have the impulse response, you can compute the frequency response using an FFT. Plot its magnitude and phase to see how the filter behaves in the frequency domain.

The (group) delay is the negative derivative of the filter's phase response. You will find that the phase is a linear function, so the delay is a constant. You just need to determine the slope of the phase (either analytically or by inspection of the phase plot).

Without any further knowledge of your desired signal and the noise characteristics, you cannot say much about a possible SNR improvement.