Would Laser Weapons Have Recoil?

The laser does indeed have recoil; however, the momentum of the particles p=h/lambda isn't very much (h is a very small number). The laser would be slowed a very small fraction.

Does laser weapons have recoil?

It was determined that the laser weapons should not have perceivable recoil based upon their in-game damage. However, when considering their ability to disintegrate targets, the recoil was calculated to be of such large magnitude that the weapons would be unusable.

Would plasma weapons have recoil?

Logically, directed energy weapons would have no recoil whatsoever. However, most of the weapons in Halo are not truly "directed energy." The plasma pistol and plasma rifle fire "plasma," which is ionized gas, and would require some kind of kinetic reaction to propel the bolts.