The main discussion about OgreKit should happen in this specific forum topic at the Blender Artists forums:http://blenderartists.org/forum/showthread.php?t=155310
Bug reports in the google code issue tracker: http://code.google.com/p/gamekit/issues/list
1)Are there tutorials or examples of how to use it?
Try to compile the trunk using cmake. The main example is trunk/Samples/Runtime, a second more complex sample is trunk/Samples/LogicDemo.
2)Is this a API or SDK or a wrapper of Ogre + bullet?
3)Can I program it in C++?
It is all written in C++ and you can use it any way you like as game engine or SDK. OgreKit includes Ogre, Bullet and it has some Lua scripting bindings and a bit more.
4)I downloaded the source and i saw a folder called 'OgreLite'. What's that? A modified 1.7 version of Ogre?
It is just Ogre trunk from a while ago, with some of the unused parts removed. It should be easy to upgrade to the latest trunk of Ogre.
5)I downloaded the compiled sample and it only has one exe but no dlls (I didn't see Ogre dlls for example). How can Ogre run without those dlls?
We link everything statically to avoid "dll hell", and we improved the cmake build files so that it compiles out-of-the-box without very little effort. It doesn't require any external dependencies.