I've not yet dug into it, but my gut feeling on looking at the description of how the static front page plugin works is as Denis-de-Berna describes...
Fold Page List is an adapted version of the standard wp_list_pages function, so the 'removal' of the 'home' link is certainly going to cause some headaches... What is surprising though is that it seems (I've not yet checked) to have been working in versions prior to 2.0.
For myself, I use the home.php file in the active theme for generating a different homepage, but this lies outside the normal 'pages' structure and so cannot have sub-pages associated with it.
I'd like to resolve this incompatibility, but if Static FP is taking away the very thing I need for FPL to work, it's going to be 'interesting'.
For piotr82, both the Fold_* plugins work to collapse the navigational hierarchies to their top-most elements (first level items), and to only expand the relevant sub-lists for the currently selected page/category. They are of benefit if you have long lists of pages and/or categories that include many levels of sub-navigation. If you do not have any such hierarchic navigation then they will be of, at best, very limited use.
On the other hand, if you DO have complicated lists of pages/categories and sub-pages/sub-categories going many layers deep, then they are, potentially, very useful in cleaning up the presentation of navigation to the minimum needed for any particular location within your site.
Hope that helps clarify somewhat.