How to calculate the noise power for a non-stationary noise? With stationary noise we have constant mean and variance (let's assume it is Gaussian noise). My first question is, how is the noise power calculated and how it is related to the variance?

Now, I have a non-stationary noise which its variance is not constant and changes periodically over time. My second question is, how can I calculate the noise power for this noise and how it is related to the time-variant variance?

Any help and remark on the topic would be appreciated.

Thank you all.
If your signal is just $n(t)$ distributed as $N(\mu, \sigma^2)$, then the expected signal power is then:
$$
p_{\rm ensemble} = E\left [ \left| n(t) \right|^2 \right] = \mu^2 + \sigma^2
$$

For the time-varying case, I'd suggest that the answer is:
$$
p_{\rm time\ varying} = \mu^2(t) + \sigma^2(t)
$$