Can I use my own versions of BLAST/Phylip/CLUSTALW/GD instead of the version that comes with TreeMos?

Yes you can. The easiest way to do this would be to install TreeMos, then delete the TreeMos directory containing BLAST, for example, and replace the directory with a symbolic link of the same name to the directory containing your own copy of the software. If you're not sure what this means, then it's probably easiest just to use the copy that comes with TreeMos.

Will the TreeMos installation interfere with my previous installation of BLAST/Phylip/CLUSTALW/GD?

No. TreeMos installs these components in its own private directories, checks that these don't exist before it creates them, and doesn't alter any system-wide configuration, so will not interfere with your existing copy.