First, would WoW look different if rendered in OpenGL, rather than Direct X? Would performance be significantly different if rendered in OpenGL?
OpenGL and Direct3D follow similar principles: A stream of vertices goes in, gets transformed (either fixed function or by a vertex shader), after transformation the vertices are grouped into primitives (points, lines, triangles) and the primitives rasterized, i.e. for each pixel the primitive covers some calculation (again either fixed function or by a freely programmable fragment shader) is performed that determines the so called "fragment" color. Finally the fragment it tested for visibility and blended into the picture-in-drawing-progress.
Later versions of OpenGL and DirectX added geometry and tesselation stages, but those are just details.
In all other aspects the ways they work are so similar, that there's virtually no difference between rendering results, except the rounding errors introduced on the vertex positions by the different clip space mappings.
Second, What is the main process when creating a game, specifically in terms of using a model created in Maya, or 3DS Max in the video game? Does one create the model, then export the model to readable OpenGL/DirectX code, with all of the shader programs exported, and all vertices and triangles created in code, and finally utilize the code in a C++/c program?
No! The model and its auxiliary data are stored separately from the code. While it most certainly is possible to store geometry in code, this is a rather bad idea and should not be done. I explained the basic idea, how a model is loaded in How to Import models from 3D software, like Maya into OpenGL?
OVerall, I'm curious on how video game designer/programmers export actual 3DS MAX/Maya models into their code
They don't. They export their models into a file format optimized for efficient loading by a 3D engine, and then the engine loads the models and auxiliary data from files. This is not some kind of black voodoo magic. The whole process is not very different from loading an image from a file and displaying it or some music playing it to the speakers. To animate a 3D model, the model contains additional control information (armatures, bones, etc.) which allow to deform it based on a rather small number of parameters (arm rotation, looking direction, etc.) Then those parameters are varied.