Any Open Source Fast Wavelet transform libraries?
you can have a look at the LTFAT's wavelet module
http://ltfat.sourceforge.net/doc/wavelets/index.php

it runs in Matlab/Octave with backend written in C. It has fairly large database of wavelet filters and new ones can be added easily.

What exactly do you mean by 


  2) Ability to run in parallel - VERY IMPORTANT


Should the computation itself be somewhat parallelized or that it should be possible to run several batches of FWT calculations? I guess that running several instances of Octave should do the trick in the latter case.