The advantage of using PCA in the frequency domain is to choose a set of weights by exploiting the cross-correlations between the signals at particular cycles.
For example, (depending on the field of application) the behaviour of the variables under study can be different in the short, medium and long run. Using PCA in the frequency domain will allow to choose weights depending on the frequency.
The difference between PCA in the time domain and frequency domain can be understood in terms of how the eigenvalues are computed. In time domain, the correlation matrix is used. In the frequency domain, the fourier transform of the correlation matrix or the spectral density matrix is used to compute the eigenvalues.
For technical applications of using PCA in frequency domain, there is a description in book by Jolliffe,I.T(2002), Principal Component Analysis, 2nd Edition. Here is a link to the relevant page.
Regarding your second question, I have understood PCA by itself to be a method of finding combinations of variables which extract the maximum information in the data by maximizing the variance of the principal components. Therefore, it does not seem to be dealing with any cyclic or frequency information in the data.