If I pause the game can I still move things around and do stuff like a turn based game which this should have been in the first place as the board game is turn based.

No, unfortunately. I agree, on a busy "day" there can me too much going on to check all the incoming messages and input all the needed commands. I would love to find a way to hack the game to either allow actions while paused, or slow down the Slowest speed setting so each day lasts several minutes/infinity.

Most of the time, you don't actually need to read every report. If something was discovered in an espionage mission, for example, it is readily apparent from mission icons, fleet icons, etc.