you asked:
"Which template style is assigned to that 'nicepage'?"
answer:
the standard template for your t4 framework is assigned:
"T4 Standard Blank"
i did not modify that template.
if you want to comprehend that behaviour, just get a new joomla setup, install
- t4 framework
- nicepage extension
create some standard pages, so that there is a any menu with submenu for that site
do "new page" from nicepage menu inside joomla
get any pre-build page as an example
save that page
go to menu and put that new page in main menu
assign that page to T4 template
see the result: there is no menu

--
to give you access to that site, how do i do that?