Glad you like it. More documentation is on the way and hopefully will be there with the next update!
Not right now. Both answers.
I don't really support playing FPS games with a gamepad and I don't play them with gamepad myself. Thus I will not be able to make a good implementation of this. It's better I don't even try.
As for keys sprites... yes, that would make sense but there is no way to do that at the moment. Maybe later.
I don’t want to hijack this thread, but want to ask you a question related to skyboxes.
What is your recommended resolution for a rectangular skymap? I’m testing it with higher resolutions like 1024, 2048. But when the player looks into the sky we can actually see the cylinder-like below. 
Do I need to change it to some other resolutions?
Note: Current skybox resolution is 2048x1024.
This is the proper behavior of this type of skybox. You need to provide your map with a proper fog color, that will blend with the top of your skybox. That's because any other geometry will be hidden by this fog and skyboxes will always be visible. If you don't have a proper fog color it will look as if skybox hides your geometry instead of blending with it. In other words: it's not a good idea to keep your background color (which is the same as fog color) black unless you have a skybox or your skybox is black at the top and bottom. There is no real fix for that. Even a cubemap skybox will have such a behavior.
As for resolution - there is no real limit other than RAM you am at. Although I'd keep it at something like 256 by 512 or 256 by 1024.