>>1
I'd be wary of using older 3D scene graphs or rendering engines. They're often built around fine-grained object-models, with poor scalability for multi-core machines. Stay away from things like Ogre 3D, Irrlicht, Unity 3D, or Babbys First Game Engine.
Unreal Engine 3 has a free community version you can get up and running with quickly, although Unreal Engine is getting pretty long in the tooth.
If you have access to Crysis 2 on PC, the CryEngine 3.1 SDK is available to you. Many universities also have the CryEngine3 source code which is available to students.
>>4
SDL is low-level and only provides basic features to handle creating an OpenGL context and frame buffer/swap-chain.