Yes, OBJ and glTF meshes are not required to include vertex normals.
If yes, is it possible for me to create light (diffuse, ambient etc) or do ray tracing etc on materials
Yes. For glTF, a mesh that doesn’t have vertex normals is supposed to be flat-shaded. The client can either compute flat normals as a vertex attribute, or compute them in the fragment shader. I don’t know whether the OBJ format specifies what a client should do in this case, but it’s technically possible to compute either smooth or flat normals.
What are standard or well-known free tools which edit obj files or gltf (bin) files ?
Blender is probably the most widely-used, general-purpose free tool for editing 3D models. If you have more specific goals for the kind of editing you want to do, there might be other tools more focused on that area.