Note that when you load Normals for a object that is perfectly smooth they index differently then when not smooth.
Here is a link to some code I have made to load a FBX file into system memory... thought it might help. DOWNLOAD LINK You want to look at "MedelProcess_Mesh.cpp" btw to answer some questions you might have. Hope this helps, remember I have no animation support in there.
SIMPLE ANSWER::
For UVs.
int uvIndex1 = mesh->GetTextureUVIndex(polyIndex, 0);
int uvIndex2 = mesh->GetTextureUVIndex(polyIndex, 1);
int uvIndex3 = mesh->GetTextureUVIndex(polyIndex, 2);
KFbxVector2 uv1 = uv->GetAt(uvIndex1);
KFbxVector2 uv2 = uv->GetAt(uvIndex2);
KFbxVector2 uv3 = uv->GetAt(uvIndex3);
For Verts.
int vertexCount = mesh->GetControlPointsCount();
KFbxVector4* vertexArray = mesh->GetControlPoints();