How can we calculate the frequency response of each filter of a Discrete Wavelet Decomposition filter bank?
The decision under the link you provided seems good enough. The main idea is:


we have impulse response of each filter
take the impulse response of the filter with the slowest sample rate as the input signal
route it back through the chain
perform spectrum estimation of the resulting signal


Division by $\sqrt2$ is for normalization only. For the given set of db coefficients their sum is $\sqrt2$, look here for explanation. It has no impact on the sense of the result I think.