Just to be clear, your tactical selection should never be random, for example if you have a morale advantage picking a tactic that provides you with a morale bonus or enemy morale malus can pay big dividends, particularly if you can encourage a situation where the enemy panics. Likewise in naval combat against an aggressive Admiral, selecting an option that decreases enemy aggressiveness or increases your own commander's aggressiveness might also be a good plan.
So examine what each tactic gives you in the situation that you're in and select accordingly.
There are left and right sides. What is the purpose of the right and left sides? Also there are two rows on each side. What is the purpose of the top row and the bottom row?
The right side of the battle screen is generally used when there are more than eight-units on a side. I have not noticed any advantage to having units there if the enemy does not so there does not appear to be any flanking bonus or penalty, unlike in land battles. However, in full-blown fleet actions on occasion it may prove advantageous to place overwhelming force on one side rather than spreading combat power across both sides evenly. Experience and the anticipated threat can be your guide for this.
Destroyer units are essentially one-shot assets so be careful when the range closes to Short and try to avoid exposing them to gunfire damage when fighting a Long.
Missed the question about the rows but I have never noticed any effect, ships get damaged by gunfire and torpedoes in both. Suspect that it's just to save space.