fftw3tbx - probably is not used anywhere
It is used in scitbx/fftpack/timing/eval_times.py to compare with the speed of scitbx.fftpack. Ralf wanted to see how much faster the highly optimised FFTW was. Not enough to implement a mechanism to easily swap fftpack for FFTW though but it has been years that eval_times has not been run. However I would not be surprised that the script provided by fftw3tbx to install FFTW from source does not work out of the box anymore. So anyway, yes, I think it can go.
dox - probably was meant as documentation, actually contains some documentation in RST, Ralf's talks from Siena, 2005, some tutorial in LaTeX, the content for the cctbx website.
It contains the code to run doxygen and produce HTML pages documenting the C++ code.
I suggest to move compcomm to dox despite the reference in 2009 paper
Why not. Best wishes, Luc