So I am going on my first hunt, and I finally found a squad of Eye Snatchers to shoot down, and I tried to use my YT-2000's Heavy Lazers on them, but it wasn't working. So I was wondering if I was doing something wrong, or if I can't use Ships against Creatures/Bandits.

you can not use ships or vehicles. You have to use a weapon and be in range..ie knife is up close, ELG is a few squares back. If you are using a squad of NPCs they need weapons as well.

Be sure to check out the hunting guide for lots of useful information.