The time next to someones name means that was the last time there was activity on that planet. Either by someone attacking them, or by them logging in and doing stuff themselves.

You should really look out for people with an 'i' (Inactive for 2 weeks) or 'I' (Inactive for 4 weeks). If their mines are setup and cranking out resources and they have little / no defence. Those are the people to raid. They won't fight back!

Missile Launchers just do their own thing once they are built. If someone attacks your planet all forms of defence can be destroyed (If the atacker is strong enough), missile launchers, lasers etc. Your mines and buildings however remain intact.