I Just uploaded a sample index.html page for my github project repo gh-pages branch. However it seems the url used to access the documentation is case sensitive. The correct url is as follows,
However if I use the same url in lowercase github displays a page not found message. i.e.
For your 4th question, I just tried to create a new repository on Github which would only differ by case to an existing one (of my own account), and I got a "Name is already taken" message. So, no, you can't have two repositories differing only by case.
(It is possible to have directories and files inside the repository differing only by case, if your file system allows this, though.)