Some questions about the intuition of the DWT
First, one should be cautious about processing short signals like these. I am unsure about the length of 3 for a3 and d3. Now, the many questions:

I would not call them &quot;frequency plot&quot;, but stacked subband plots. They are just illustrations of the behavior of the wavelet coefficients. For each subband, different scalings may be used. Another rendering is stacking the intensity of coefficients in a image. For the interpretation of the points: the coefficients in each subband at located in time and scale, so the interpretation in $[\pi/2T, \pi/T]$, $[\pi/4T, \pi/2T]$ is only approximative (because of aliasing, subsampling, etc.).
No, one is concatenating chunks of coefficients in different subbands and at different rates
Yes, subbands of a given WPT can generally be interpreted in dyadic portions of the time-scale axis
Haar wavelets (2-tap filters) have the rare property (among standard wavelet filters) they don't overlap at a given scale. For longer filters with 2-band wavelets, those filters overlap, and yield troubles at the extremities of a finite-length signal. There is a lot of works on non-expensive expansions, relaying on the symmetry/antisymmetry of the wavelet.