It would have to be kind of large wouldn’t it? I.e. about 864,000 miles in diameter to completely obscure the sun. Smaller if you’re will to settle for just dimming it somewhat.
Not really. If you stand outside and look at the Sun, you can shield your eye with a nickel. Just put the device in space far enough away and it can be just a few hundred meters on a side, mostly to insure coverage because of the movement of the Sun and the target, which could be hundreds of light years away.