The turnbuckle and chains modification is simply to limit side to side movement of the extension bar in the receiver hitch, due to the normal clearance fit between the nesting tube sizes. All hitches have this normal amount of slop. On a standard length ball mount, the slop isn't much of an issue. When the ball mount is moved 3 or 4 feet out on an extension bar, the slop becomes much more noticeable.
There is nothing wrong, bad, or unsafe about doing the turnbuckle/chains mod to limit the side to side slop when using an extension bar.
Yes, the trailer's safety chains should be run from the trailer tongue, all the way to the truck's receiver hitch.