White Gaussian Noise Spectrum and Power
If I want to know the power of a certain frequency in the signal (not in a range of frequencies), can we say that the power of each frequency in the signal is exactly No/2?

No, BUT: You mean the right thing, you just say it wrongly:
The Power Spectral Density is constant – a single frequency doesn't have any power; it has a &quot;power per bandwidth&quot;! To arrive at a power, you need to integrate the density over a non-zero mass of frequencies.
(This is kind of an important distinction to make – only infinitely long periodic signals, e.g. sine waves, have power at a single frequency; everything else has a &quot;power distributed over frequencies&quot;.)

The total of power of additive white Gaussian noise is infinity, what does this mean? Is it reasonable to assume that the noise added to the signal have an infinite power?

Yes. Notice that you're never dealing with a truly white Gaussian noise in continuous-time systems (luckily for the universe, I might add); it's always approximately white for some bandwidth. Everything else is physically impossible – but rarely matters. Example: the thermal noise you can measure over a resistor is the classical example of white Gaussian noise in systems. However, it's not really white – the power density decreases at very high frequencies. But that's totally irrelevant to your observation – your measurement doesn't go into the terahertzes.
In time-discrete systems, things look different: for a sampled time-continuous stochastic signal (noise) to be white, it's sufficient that the original time-continuous signal had a constant PSD over a bandwidth. So, there's no physical problem in the time-continuous world. Since a discrete signal is just a sequence of numbers, there's no concern for &quot;physicality&quot; anyways.