Energy normalization across wavelet subbands
The report under reference is A Really Friendly Guide to Wavelets by Clemens Valens, 1999.
The title of the question might be misleading. The energy normalization concerns the wavelets themselves, required to have the same energy, whatever the scaling and the shift. This is useful for theoretical and practical reasons (algorithmic/computational stability,  and several statistical properties).
If function $\psi(t)$ is of finite energy $\|\psi\|_2^2$ (or square integrable), then by a change of variable $t\mapsto st$, you will find that  $\psi\left(\frac{t-\tau}{s}\right)$ has finite energy as well, and that $\|\psi\left(\frac{t-\tau}{s}\right)\|_2^2 = |s|\|\psi\|_2^2$. For the wavelets to have the same energy, you should divide by $1/\sqrt{|s|}$.
An  interpretation is the following. The energy of function is homogeneous to a rectangle with a time span horizontally, and a square in amplitude vertically.
You want to keep the area of the rectangles constant for each wavelet. So if you dilate the time by $s&gt;0$, you should contract the square in amplitude by $1/s$, then the amplitude by $1/\sqrt{s}$.
For question 2, the spectrum will be stretched/shifted accordingly, if you compute the Fourier transform of $\psi\left(\frac{t-\tau}{s}\right)$. The scaling property of Fourier is mentioned in Clemens Valens tutorial at Equation 14:
$$\mathcal{F}\left(f(at)\right) = \frac{1}{|a|}F\left(\frac{\omega}{a}\right)\,.$$