I have no texture image but colors and shading in materials. I want to export it in fbx so those materials(no image texture) with my shaders will be applied in the result. I'm absolutely new to shading and baking stuff so I would like you to explain it to me if you could. There's also a little bit of glitter on the material made by Voronoi texture just for the record.
If you want use this model in a new blender file, save the file with this model. Open the new blender file that you want to import it into. Select File then select append, navigate to the old file where your model is, double click on the file name and go into objects, select your model/object name and then press the append button and your object should be imported with the shaders that are assigned to it.