Power and Energy Computations in the Frequency Domain
How do you calculate the power and energy of a signal given only the frequency domain form of the signal function?

For power you do it in exactly the same way that you would in the time domain;
Time domain: \$ P(t)=V(t)I(t) \$
S-Domain: \$ \tilde{P}(\omega)=\tilde{V}(\omega)\tilde{I}(\omega) \$
If you don't know \$ \tilde{V}(\omega) \$ and \$ \tilde{I}(\omega) \$ Then the situation is the same as if you were to try and calculate the power in the time domain without knowing \$ V(t) \$ and \$ I(t) \$, it is not possible.
For energy you pick any number you like..
The s-domain does not care about time. If we assume that you have a signal at 1kHz with a power of 1W. if you observe this signal for 1s in the time domain then the energy is 1J, is you observe it for 1000s in the time domain then the energy is 1kJ.