Yes it cannot be physically done. Every lens is designed to project the image on a specific distance (distance from lens to sensor), this is called the flange ditance. Now when you put an adapter or a speedbooster, the lens will be pushed away from the sensor and will not be focusing on its correct plane.
Well, you're partially right. That makes it harder, but not impossible. With a teleconverter, the lens gets farther away from the camera, but the focal plane shifts backwards by the same amount. With a wide converter, the focal length is reduced, so without additional correction, you'd have to somehow move the sensor closer to the lens, which is impossible (obviously). You can, however, compensate for that by adding extra optical elements that shift the focal plane further away.
The good news is that Kodak actually designed a telecompressor a couple of decades back that did exactly that. The bad news is that they patented it, and the patent (US5499069) didn't expire until four months ago, which is a big part of why such devices aren't on the market today. From the patent claims:
1. c) an optical adapter located between said lens barrel and said camera body for providing a smaller size image than said objective lens system provides when mounted directly to the camera body, said optical adapter including a lens attachment optical system, a front lens element of which is located in front of an image formed by said objective lens system exclusive of the lens attachment optical system, said lens attachment optical system having a plurality of lens elements which have radii of curvature and spacings sufficient to create a back focal distance to clear the SLR camera body mirror.
More to the point, Kodak's patent covers only situations where you have to maintain a long back focus (flange focal distance). Wide converters that adapt lenses with a long flange distance to cameras with a shorter flange distance aren't affected by that patent, which is one reason that they're readily available. (That, and they're a lot easier to design.)
Now that the Kodak patent has expired, it seems fairly likely that we'll see these appear on the market in the not-too-distant future, assuming anybody is willing to spend the time to design the (significantly more complicated) optics.
2-the lens must be designed to cover a larger sensor than the camera's sensor it's being used on, for example, a full frame lens on an APS-C body, because the idea of a SB is that it focuses the large image circle down to a smaller circle, giving an increase in light density and wider fov. If you use an APS-C lens with a SB on an APS-C body, the SB will shrink the image circle of the APS-C lens to a smaller m34s-ish image circle, therefore you will have a huge viggentte.
This part is correct. The only way to avoid that is by putting a wide-angle adapter on the front of the lens, rather than the back, which is generally undesirable for any number of reasons.