Is it possible to give Fighters a beam laser?
(Like the ones the Advent Bombers use in SoaSE)
Yep. For example, the Unity mod, by Darkstar076, has tons of frigate weapons on fighters. Im very new, but i donk think fighter beams are to hard to implement (probably just messing with a text file :-)). However, if you want replicas of that bombers laser, i think you would have to find the imagery and sound files for it to replace the standard beamlaser.DDS files. Thats all i think i know 
Have Fun!
Aaaaand, PI Mod drones have ONLY beam weapons, imagine some bits flying around with minilasers cutting everything ^^
Nomad lasers on fighters!!! Awesome XD!!!
Almost 95% (if not 100% i cant remember now a weapon that is incompatible with fighters) of the cruiser/frigate weapons can be used on fighters, the only difference is that u will never see the weapon turret, thats all. U can imagine little fighters with tractor beams, or fighters with big lasers, powerful shotguns, strong beams, lightning rays, etc, everything u want. The good thing is everybody can “invent” new weapons, they are not restricted to the modders.