Ah, no, no Omega beams yet. Just Heatwave's heatwaves.
After you complete the game once, enemies will start resurrecting as Black Lanterns. ... And so will the heroes you use, if they die.
The Batclaw doesn't make any sound, unfortunately. You can use it to grab enemies (something like Scorpion's spear from Mortal Kombat), and it can move some objects, like destroyed cars or statues.
I went and tested it after some of the questions in this thread, and I found that I could stand on top of some of the shorter buildings and use the batclaw to grab destroyed cars from below to hit enemies.