You can move ships in 3d if you like and they will travel pointing up or whatever is appropriate so you it is possible to have ships face in any direction.
There are different combinations of camera modes and one of them allows you to rotate it 360 degrees around any object. Weapons and some special actions are directional.
Typically, weapons exist in one of 4 banks that fire out in a 3d cone. For example, if the weapon is in the forward bank it can't hit things to the side, or behind it. The AI knows which bank is currently optimal and will orient as neccessary to bring the most damage to bear. A rough guideline is some ships are primary forward firing (massive beam weapons), broadsiders, or omni-directional (anti-fighter frigate with equal weapons all over). Another consideration is how to position your ships to maximize the damage from all banks. A battleship that is only firing forwards at a single target is losing 2/3 of its potential so you would want to move it so it could fire left, forward and right, at 3 seperate targets.
Finally, as Yarlen said, this may change in the future based on feedback from you guys 