Yes, it is. General relativity tells us there will be two main effects - gravitational red-shift and gravitational lensing. Since the light originates from the bottom of a gravitational well, as it escapes the well its frequency goes down, red-shifting the light. read more
Yes, the gravity of earth does affect a laser when fired from earth but to the slightest extent. In general, for a body to escape earth's gravity, it needs a velocity of 11.2kms per second which is called as the escape velocity of earth. Laser beam has a velocity of 3*10^6 kms per second. read more