If you can point us to the actual camera on e-bay we can see if it is any good.
The reason it says 3mp, then 2mp, then 1.3 may be that cameras can usually have settings which define how good the picture is and how many pixels the picture will use.
So a camera may have a setting of "top quality", "good quality", "average quality", "low quality" and so on. All this is doing is changing the number of pixels that will be used in the picture.
Obviously the lower the number of pixels the lower the quality of the picture.
To answer your last question, NO it is NOT a 12mp camera.