The black borders around the edge are typical of CRT screens. They aren't damaged and there's nothing to fix. This is just the way they are.
The reason you are seeing "color" behind the"dot" missing in each line and why your Blu-rays seem to go beyond these borders is because of overscan (which is also normal for CRTs). If you are able to get into the service menus for these TVs you may be able to adjust the amount of overscan to recover some of the picture/pixels that are going beyond the black border. The border however will always be there.
Just a warning. If you choose to do so, be careful anytime you are in service menu mode. One false move and you may screw things up and not know how to change them back.