Weird, the site works here. What kind of error do you get?
For general game scripting, I would recommend C# but for "advanced" features I'd definitely start leaning towards C++.
Since you're interested in creating something different from the default CryENGINE FPS sample, I'd advise to checking out our minigame sample and going from there. The full guide on setting it up can be accessed here; Installing the MiniGame sample project
Let me know if you still can't access the docs site