Menus are okay now as I reduced the top margin on every page of the element just under the menus. That (initially -45px) was what was causing the problem.
I think everything is more or less okay now. The menus too are fixed.
EXCEPT.. please view homepage (www.bhawanipurdesignacademy.org) using Firefox browser. Scrolling to the bottom makes it jump continuously. Why is this happening? Was earlier happening too.