I don't know how many times my ship has stopped to die because of messages coming in. Unless I am failing to see where to shut this off at, those messages should blink at the bottom of the screen or something and not come up till I (the captain, after all) say so. I was doing the fleet battle at Starbase 24, and the moment I was prompted to do the mission, my engine stopped, and just a little under 10km away a huge bunch of enemy ships spawn. I was toast in a matter of seconds cause no one else was around.
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Just look through the options menus, it's probably on the HUD tab or something.