Well, I had a long post to explain the matter, but the forum ate it
twice, so I will keep this one short.
So, in general, fire modifier is most important if you want avoid casualties?
No.
The best ways to reduce casualties are:
(1) to get the "tactics" bonus (by staying below the CAV% treshold).
(2) to shorten your frontline by using ART.
(3) to lower the enemy offensive capacity by fighting in difficult terrain, causing attrition and depleting his morale before the decisive battle.
(4) to shorten battles by increasing your offense via discipline, a good general and maximized combat power per square.
But fire has the advantage that it is resolved before the shock phase (once again, this was changed a few times already).
So the first 3 days of combat are fire - and if you have an army with good firepower, you will deplete the enemy numbers and morale, decreasing his combat power during the shock phase.
This is especially devestating for all-CAV armies: They are only powerful during the shock phase, but if the enemy has a good roll during the first fire phase, the CAV regiments are decimated, in a worst-case scenario useless before they could even inflict reasonable damage.
Units from 2nd line can shot (ART) while 1st line fighting and, for example, full calvary army will do nothing on 2nd line?
Yes. Only ART can fire, the rest will just sit idle and do nothing.
The game follows a certain procedure when setting up the battle (I am not 100% sure, but that is - in general - how it works):
Unit priority:
First line: CAV> INF > ART
Second line: ART > INF > CAV
Flanks: CAV > INF > ART
Maneuver:
INF: 1, can attack a unit in front of it and one square to the left or right
CAV: 2, can attack a unit in front of it and up to two squares to the left or right
ART: 2, can attack a unit in front of it and up to two squares to the left or right and may fire from the second line into the enemy square in front of it
Units will always attack the closest enemy.
Placement:
(1) Starting from the middle, the game will place as many units head-to-head as possible. CAV is placed first. If there is not enough CAV to fill all squares AND the flanks (!), the game will use INF instead. INF will always be placed in the center. ART will only be deployed in the first line if there is no covered square left in the second line. A covered square is a square with any INF, CAV or ART unit in front of it.
(2) When the first army runs out of melee units (including ART that has to be placed in the frontline), the game will add flanking units for the army that still has melee units left. It will place up to 2 units on each flank, starting with CAV. If there is not enough CAV, the game will use INF instead. But remember: The outer flank square can only be filled by CAV!
(3) The game will fill the second line, starting from the middle. It will place as much ART as possible, afterwards it will place INF and CAV as reserves to fill the remaining covered squares.
(4) If there are still melee units left, the game will place them further to the left and right. These units are out of range for combat and act as reserves.
If a unit breaks and a square is no longer occupied, the game will move the unit to fill the gap. I am not 100% sure, but iirc it first uses units from the second line. If there is no second line unit left, it will move units from the left or right inwards, moving all remaining units in the process. Since this will create another gap, the next unit will move, and so on.