Yes, you can use the OpenGL API by itself. You have to use your operating system's APIs to create the OpenGL window, get input, measure time and so forth. Windows, OS X, Linux will all have their own ways of doing these things.
- GLUT, SDL, SFML, and GLFW are wrappers around the operating system parts. Each of them provides a cross-platform way to create the OpenGL window, get input, measure time and so forth. Even if you're only on one platform, though, they probably offer a simpler interface than the operating system APIs, therefore may be easier to code for.
- GLEW and GLEE are libraries for helping with OpenGL extensions. You can set up extensions yourself, but it's a huge pain, especially on Windows. GLEW and GLEE have done most of the busywork for you.
You don't have to use any of these libraries, but you'll probably make life easier for yourself if you do. Note: pick one library from each list. For instance, you could use GLFW together with GLEW. Don't use both GLFW and SFML though. Likewise, don't use both GLEW and GLEE.
Loading a map and flying a camera around isn't too difficult. You can certainly do that without an engine. As a newbie to 3D graphics it will take you a little while to get right, but it's certainly doable. Try http://www.opengl-tutorial.org/ for some tutorials to work through. They use GLFW in all their code samples. They also use many OpenGL extensions, so you will need GLEW (or GLEE, but it's not as up to date anymore). If you work through those, by the time you get to Tutorial 8 you should be able to load a map and fly a camera around.
As for modeling, it takes practice. Drawing also takes practice. I don't believe there's anything that "you can't do it unless your born with it" - everything is an acquired skill. The people who are "talented" are usually that way because they've practiced a huge amount of time over years, not because they were somehow born with an ability you weren't. Anyway, the point is that if you keep working on improving your art and learning more, you will get better. It might go slowly, but you'll get better at it if you just keep practicing.