Hello, D.Realms, welcome to the forum.

The software we tend to use for vectors in this site is one of the Xara applications, the current flagship of the fleet being Xara Designer Pro. Xara3D is a standalone app which takes vector shapes and extrudes them, giving a solid 3-dimensional look. Such solid objects can be given a paint job by importing a texture in the form of a bitmap of some type, like bmp, png, jpeg, etc. The solid objects can be animated, but the shapes making them up cannot be edited in Xara3D itself, except for extrusion depth and type and size of bevels.
Xara3D is unable to use transparency in these textures, but in exporting an image or animation, it can make the background transparent, if the target format itself permits it.

The avatar you refer to, (the spinning hollow earth) is quite a complex construction, definitely not for the faint-hearted! There is a tutorial describing it here.

Mike