What tech tree are you using?  In the Terran tech tree there are techs like "Shield Support Systems" and "Point Defense Support" and "Armor Support Systems" that let you build military star base modules to assist the defense of your ships.  There are similar "Beam Weapon Augmentation", "Missile Augmentation" and "Kinetic Augmentation" techs that all you to build star base modules to assist the offense of your ships.

For your second problem, are you already using the antimatter for something else?  In the upper right of the main map there is a display of the resources you have, if you hover the mouse over them it will tell you what star bases are mining them and where they are being used.