At first, I want to admit that Rise of Prussia is wonderful game. So deep and at the same time beautiful: simply great. Also good to see, that the game is still worked on. It deserves it!
I spent some hours trying to understand what I could do to shift battle outcomes to my favor.
I read a lot, especially this one. (Thanks to JacquesDeLalaing: I learned a lot!

Still, there remain some questions.
I learned that artillery, justed stacked with the column, fires on the "healthiest" element around. I run some tests with the tutorial scenario and checked the battle log. I couldn't find out, how the "health" of an element is determined by the game. Wiki says, it was "hit points times battle signature". I don't understand the meaning of the latter (and most elements that haven't already suffered losses, have 10 hitpoints, haven't they?). Can someone help me?
(I my tests saxon cannons always fired on a unit of my best brigadier, even if there were grenadiers in other units around (which I would suspect to contain the "healthiest" elements).
Another question is: If commitment to battle (i.e.commitment of elements to battle) does not take into account the unit of the element, why does the detailed combat report list participating units? This seems strange to me.
Related to this: since the enemy targets units, not elements: How are the losses spread among the elements? Is it random or is it always the healthiest (or healthiest comitted) element, that suffers?
Another question: Are cohesion losses calculated daily? Will the engine know, if my troops have traveled a long way to the field of battle?