There are three ways you could construct a model in Blender:
- Separate objects (two surfaces),
- one object with separate mesh parts (two surfaces),
- one object with one connected mesh (one surface).
Animated deformations on a mesh mean moving vertices so it describes a new form.
Intersecting geometry means either separate objects or separate mesh parts that have surfaces going through each other, but aren’t connected so that they stay as two separate surfaces.
In 3D printing it means that each part has to be manifold, and since surface thickness is 0, two clearly intersecting parts can describe one solid. Not all slicing softwares can interpret those though. If it can (like Slic3r), it can be a beneficial, because you don’t necessarily have to connect the geometry which makes constructing and refining the parts easier, which often need to be high resolution as only real geometry is interpreted. On the other hand, if you want to describe a hollow model, that becomes a problem because there are multiple surfaces describing one solid instead of just one. When it’s just one surface, it only needs another parallel surface to describe the solid casing in a hollow model.
With deformations you likely need to connect the geometry because as they’re deformed, the two parts tend to get separated, which looks bad when a surface is supposed to look like one connected one, or something needs to stay inside a form.
Self-intersections would be bad. Those are connected surfaces that go through themselves. Like folding a paper so it goes through itself, but without making any cuts. Can’t have that.
There’s no such thing as UV images or UV textures. There are UV maps, which contain 2D representation of 3D coordinates and go with the mesh data. Images are images, but images that are made to control specific material properties are called texture maps. Each are often named to tell which one it controls.