Calculating PSD, Cross PSD by using FFT outputs
Cross PSD (fourier transform of cross-correlation) is $X(f)^*Y(f)$, so it will $(a-ib)(c+id)=(ac+bd)+i(ad-bc)$. I think you missed to take conjugate like you previous question (Calculating Cross Power Spectral density between two complex signals). 

Cross PSD tells a lot about correlation between two different signals. If Cross PSD is white (meaning near flat at all frequencies) with very low value implies both signals are uncorrelated. If $x$ and $y$ are input and output of a system, you can measure the coherence between $x$ and $y$. The relationship between PSD of $x$ and $y$ for the LTI system $h$ is $G_{yy}(f)=|H(f)|^2G_{xx}(f)$. You can read more at https://en.wikipedia.org/wiki/Coherence_(signal_processing)