A laser is just light, so the effect on the diamond should be just the same as if any other type of light shines through it. You might get a cool effect, though.
The green laser pointer will not be harmed by pointing it at the diamond. The diamond will not be harmed either. Remember, though, that the diamond will melt at 3550 degrees F so keep it out of house fires or car fires.
No the laser light will not do any sort of harm to the diamond. However The laser light can and will reflect off of the diamond in multiple directions. The lasers beams reflecting off the diamond however can cause damage to peoples eyes. Some damage is temporary and some damage is permanent .
A laser pointer is just light, no.. a laser does conduct heat. if you read good enough on the web a laser can pop a balloon, light a cig, or even kill an ant. Now if you have one of them cheap 5mW Lasers, they wont do any harm.