Why are the edges of the shadow so bright?
Look at it (pun intended) this way: your diverging lenses are making the central area darker because the irradiance, i.e. energy per unit area, is reduced. But that energy doesn't disappear: it has to go somewhere! In this case, at least some of it is observed to arrive in that "border" region which is thus brighter than the rest of the scene. This area gets both the direct light and some of the diverged light.
Why is the region of the lens appearing dark (although I see things clearly when I wear them) ?
The lenses you are wearing are for short sighted vision because they are diverging the light that is why the light is not inside the region of the frame. You see clearly because they are made specifically for you :)
And why are the edges the brightest part of the wall ?
actually it is not necessary for edges to be the brightest. It is only observable at a certain distance from the wall and the brightest part coincides with your edges of the frame. :)
Hope it helps