You only get AI ministers turned on if you load an empire file that has them turned on. If you create your own, you will not have any AI ministers enabled.
Complex troop design is still important. Rate of fire and range do no matter on weapons though. Total hit points (including shields) are used to determine how long it takes a troop to die. Damage at range 1 of the weapons determines how much damage each troop does to the enemy every round. To hit bonuses (on weapons as well as combat sensors and ECM) have some effect on troop combat, though I am not sure of the exact details there.
Components like Afterburners that provide X bonus combat movement give the ship +X movement in combat. That ability is not rounded. As for the base combat movement, it equals total strategic movement divided by 2, rounded up. 6 strategic movement gives 3 combat movement. 7 strategic movement gives 4 combat movement.
Check out the Newbie FAQ, which is stickied at the top of the forum. It has answers to almost all of your questions, as well as 100s more.
