The targeting laser is a special case. In all of my tests (let's say an Ulysses), it always shoots out of the right side. If you combine it with another weapon, you get one laser from the right and ONE (and only ONE) weapon shot from the left. Let's just say that using the Erinyes with the targeting is a rip-off.
Next, if you link both banks or Targeting Lasers, if fires only the one on the right. I'm not sure about damage though.
After that, I created a extra gun for the Pegasus, and put the laser on the top, middle, right above the cockpit. Now that worked. I have a independant laser firing from the top, and if I combine it with the second bank's 2 guns, it fire whatever your Pegasus is carrying, with the laser on top. That works... sort of.
About damage, remember that beams always bypass shields. I had to reduce damage levels to 0.5-0.8 on the targeting to keep things balanced. And no, the Targeting never drains energy, never has a powerup/powerdown, and has no refire delay. As for range, I have no clue. I thought that it keep on going forever, considering lifetime values don't affect it.
Now, on the side note, I found that the targeting is a lot harder to aim than most guns (unless you make it super thick). It always flies in a straight line, unlike the guns which "fall" or "climb" with your ship. Just not used to it, I guess.