When I convert my fonts into woff files (using font2web), it produces a number of other files, mainly css and svg.

If I just place the woff file the font doesn't work.

Do I need to put these additional files in the fonts directory (or other directory) of fancy product designer?

There is no need for the other files, the .woff should be enough. Quite often downloading the font files from another source and using another page for the conversion helps.