2VDV_forever: I answered your questions, but I forgot those answers at home :) In short, here are the answers to the first two:
1) Yes, they depend on it. You can predict morale and luck drops after a couple of rounds of damage, provided you are already familiar with the battle map;
2) In Fireball's task, luck doesn't necessarily come to the peasants. Quite often, it drops on the archers in the counterattack! Also, dragons can lose morale, and the peasants simply won't survive until their turn. There are also many other possible scenarios: for example, a catapult breaks down the wall in the first round, or gargoyles lose morale after a berserk attack. But you are generally right: there is a limited number of battle maps, and, accordingly, the probability of repeating one of them increases significantly. I assume that the presence of a catapult significantly reduces the number of possible maps. I will try to calculate or at least estimate this number.