So I have been trying to discover this for years, read the whole little book that came with the game but I never knew how to increase my fire power with the anti-matter thing...

Can someone help me out?

Also I'm stuck at "the gift". I just do 1 damage per hour when shooting at the back of the ship where supposedly the shield gen is...

On the engineering screen select the antimatter injector. There'll be a small checkbox next to the output graphs. Select that to boost the antimatter input into the engine. Be warned that leaving it on too long will cause your reactor to explode!