Why are Github project document page urls case sensitive? What are the negative effects?

If you have a personal github page (username.github.io), you can create a folder inside this repository with your project name in lowercase, and inside that folder create an index.html redirecting to original url. As example: https://github.com/MiguelPynto/MiguelPynto.github.io/tree/master/shiftdisplay

I am not sure this is directly related to GitHub.
The w3c standards does mention:

URLs in general are case-sensitive (with the exception of machine names).
There may be URLs, or parts of URLs, where case doesn't matter, but identifying these may not be easy. Users should always consider that URLs are case-sensitive.

In other words, you cannot be sure what OS is behind the web server you are accessing (a case-sensitive Linux one, or not a case-sensitive one with Windows, as described in the article "Are URLs Case Sensitive?").

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.)