When I'm logged in e-demand like a manger, load of the page manage_proj_edit_page.php failed, whereas when i'm logged like administrator the page is OK.

I think problem would come from line 246 page "manage_proj_edit_page.php":
foreach ( $t_projects as $t_project ) {
if ( in_array( $t_project['id'], $t_all_subprojects )
|| in_array( $f_project_id, project_hierarchy_get_all_subprojects( $t_project['id'] ) )
|| ! access_has_project_level( $t_manage_access, $t_project )
) {
continue;
}

It's Ok if i replace the last $t_project by $t_project['id']

foreach ( $t_projects as $t_project ) {
if ( in_array( $t_project['id'], $t_all_subprojects )
|| in_array( $f_project_id, project_hierarchy_get_all_subprojects( $t_project['id'] ) )
|| ! access_has_project_level( $t_manage_access, $t_project['id'] )
) {
continue;
}

I hope this will not make functional regression