One civvie mining complex = all that? That's good to know; I'll probably start pulling minerals from 'em, then.
So, about missiles.
How do I shot stuff? I've made my missile ships, made the task group, assigned launchers to fire controls and missiles to launchers, so how do I tell my ships to shoot at the offending vessel?
Choose a hostile from the contacts list, assign it to the missile fire control then click "Open Fire"
Keep in mind that the targetting isn't very intuitive. There are checkboxes (I believe in the Display tab of the system view) that let you see the FC and missile ranges of your ships, as well as one in the Sensors tab that lets you see your AS ranges. Give a move order to your ships that will put the enemy ships inside of your missile range, open the combat tab after this (make sure to open it AFTER you get the contacts in your FC range), then assign targets to fire control systems like you would assign launchers, in the bottom left. Once you're in range and targets are assigned for all ships, click the Open Fire button for the FLEET controls. Advance a five-second tick. If the missiles launched, have the ships cease fire, otherwise you'll get constant interrupts from your ships about not being able to fire while reloading, which will keep you from advancing time in any reasonable amount. Keep in mind how long your launchers take to reload, and be ready to open up the combat tab again shortly before that, and then fire again.
Also, sometimes the game gets buggy and has contacts disappear; just advance a five second tick.
Remember, ALWAYS close the combat window after actions, as it needs to be refreshed to be accurate. So if you keep it open after launch, and your launchers take 200s to reload, and you go back 3 minutes later, it will still say Reloading (200s), but if you close it and reopen it they will register as ready to fire. Also, ALWAYS remember to cease fire after a launch, or the game will be pretty much unplayable because it will interrupt all turns to tell you that the launchers are reloading.