I believe that it has position "locks". It definitely isn't free 360 degree movement.
Mine was. And sure it was
supposed to lock into place, but that plastic piece of crap had a very loose definition of "lock".
Square monitors would be suitable for both vertically and horizontally oriented games.
No they wouldn't. In an FPS for example it's far more critical to have a wide horizontal field of view than vertical. You rarely need to look up or down.
Overhead games (think RTS) look stupid in widescreen because you see can further in X than you can see Y.
Most RTS' are angled isometrically, so the visible area is roughly square. And
well designed HUDs are put on the side (see Command & Conquer series).