I will try to answer some of your questions...
"For those interested in the internals of the UV mapping process, I found an application which has been very helpful: UVMapper."
Have you tried using the Unwrap UVW modifier that comes with 3ds max? It also displays the UV mapping and allows for editing/creating UV maps for any max object. If a UV map exists for any imported object, that UV map will be displayed by clicking the "Open UV Editor" button of the Unwrap UVW modifier.
"Several questions come to mind. Is this process followable by peeking at the innards some file(s) and seeing the actual numbers?"
The Unwrap UVW modifier provides a visual presentation of the uv map and will show which UV tile (i.e., 0,1) the map is in. From your questions, I think you may be confusing the UV tile numbers (i.e., 0,1 .. 1,1, etc,) with the location of the texture map pixels within a specific UV tile.
"Once the UV map is completed, can it be used by another application?"
Yes, but some applications do not accept UV maps with errors in them like overlapping UV coordinates. Good UV layout is important and there are a ton of videos on the internet on how to do this in 3ds max.
"Are Albedo, Normal, Gloss, Displacement, etc. types of UV maps? (I was under that impression, now having second thoughts)." No, you are confusing 2 different concepts. Albedo, Normal, Gloss, Displacement, etc are different types of Texture maps in a Material. Each of these texture maps would rely on the UV Map that is created for an object.
"My main doubt was this: Suppose that I buy a model on the Internet. It comes with the appropriated textures which can be readily applied with our favorite 3D application. Then, the original model is subjected to some sculpting. In my case, it was a bulldog which had its legs and back repositioned. How are the new 3D points kept in sync with the 2D coordinates?"
Actually, in my experience, any change to the geometry of an object like sculpting can potentially mess up the UV layout. I always check and then tweak the UV Map layout in the Unwrap UVW editor after making any change to geometry.
Hope this helps.