Can we calculate moments (mean, var, skewness, kurtosis) of a signal in frequency domain?
If your time series $x(t)=s(t)+n(t)$ where $s(t)$ is a deterministic signal,and $n(t)$ is independent Gaussian noise,  it has a pdf of the form
$$
p(x(t))=\frac{1}{\sqrt{2 \pi} \sigma} \exp\left( -\frac{1}{2} \left(\frac{x(t) - s(t)}{\sigma}\right)^2\right)
$$
the first moment is
$$
E\left\{ x(t) \right\} = s(t) 
$$
which is NOT the DC component of the Fourier Transform of a sample. The first moment is not a constant and the time series is not WSS, and the first moment is not equal to the time average.