Earlier quoted context omitted.
Nope: http://en.wikipedia.org/wiki/Horizon#Distance_to_the_horizon
Yep. Depends on where the laser is fired from, and it depends on the target. Lasers can absolutely fire 300 to 600 km.
Lasers can fire all the way to the moon, and it might be a great idea to put military ones on top of mountains one day, depending on the weather, but if we're talking about lasers on ships...the USS Nimitz (the largest aircraft carrier class) has a height of about 36m above the waterline, so the distance to the horizon is something like 20km or ~13 miles.