I'll toss a general reply, probably won't answer all your questions. Tweak nodes in general are created when you add a deformer to an object. At that point, the shape node of the object is "duplicated", with the original shape node becoming the "intermediate object" (and it is hidden, both from view, and in the Outliner), and the "new" shape node becoming the "deformed shape". The tweak node lives between the two, and stores most component level deformations. I know vertext tweaks live in there, but face, and edge tweaks may live in there as well. If I remember right, UV's get their own special tweak node. By default, Maya will only generate a single tweak node, even if the object has multiple deformers. However, when creating deformers, depending on the advanced options set, new tweak nodes can be generated. How, at that point, Maya knows which tweak node to use when deforming componenet level goemtry, I cannot discern, nor looked into. At one point I asked AW how I could add multiple tweak nodes to my object. My thought being I could store deformations in each tweak node, and animate the envelope of each tweak to inturn animate the facial motion of a character. I remember it not working... but not the exact why... possibly because the tweaks had to be chained together, and once one was generated, you could't go back and adjust it, since all new tweaks were added to the most recent tweak. Or something like that 
It was a lont time ago....
