Material001 second attempt There are buttons on the r.h.s. of Blender which are starting from bottom:
Material properties
Object Data Properties
Object Constraint Properties
Physics Properties
Particle Properties
etc.
Now, in Material Properties I can add Materials like this:
Material
Material001
Material002
etc.
Now I want to find in which one of the buttons listed above there is a menu offering an existing
Material001
so that I can create a link to this particular object named Material001 and make use of it and its properties like color.
Not sure if I understand your question about the other property windows, what you may be looking for is the shader editor.  You can access it by going to the shading workspace at the top, and you'll find the bottom window is already set up for editing materials.

This MAY be related to what you're wanting, because you can access UV coordinates here, etc.