Power spectral density vs Energy spectral density

I read the following on Wikipedia:

Power spectral density:

The above definition of energy spectral density is most suitable for transients, i.e., pulse-like signals, for which the Fourier transforms of the signals exist. For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral density (PSD), which describes how the power of a signal or time series is distributed over the different frequencies, as in the simple example given previously.

I don't quite understand that paragraph. The first part says that "for some signals .. the Fourier transform does not exist".

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  For which signals (in the context that we are discussing) does the Fourier transform not exist, and we therefore need to resort to the PSD rather than using the energy spectral density?

  
  



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  When obtaining the power spectral density, why can't we compute it directly? Why do we need to estimate it?

  
  


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  Finally, on this topic, I have read about methods that use Kayser-windows when computing the PSD over time. What is the purpose of these windows in PSD estimation?