Yes, that is the rear sway bar. It is held on by 4 bolts and locks in the lower control arms. You can remove it and still drive the car, but it will be a little more sloppy feeling than usual. The v6 cars came with thinner front sway bars and no rear sway bar, so it should still be safe to drive until you get a replacement.
As for a replacement, a stocker would be fine. There are plenty of companies that would be happy to sell you stiffer sway bars, but unless you plan on fiddling with the suspension and doing auto-X or road racing, you'd probably be best with stock. If you do go aftermarket, remember that a stiffer sway bar in the rear will make the car oversteer slightly more.. which can be dangerous. Probably you would never notice that though.