Hopefully fixed for the next release. The double printout is just due to printing once during calculation and printing again after the value has been calculated. The during-calculation damage should have been suppressed from being output (since only the final damage value is the one that matters).
Burn damage is just a random 3-6 base damage for a set number of turns. The turns tick down twice if the target is more resistant to burning damage. For the moment, when the damage magnitude is calculated, the attacker is the first opponent (if multiple opponents, whether or not they have been defeated)--this may change in the future, but currently the person who caused the burning effect isn't tracked on the effect itself.