#1 is the rule that trumps all others for my lucky. ANY d6 can be rerolled by EACH player during EACH phase of EACH players turn as long as your mr lucky is alive.
this means player 1's turn and he declares a charge with a terror causing monster, player two fails his leadership check and chooses to reroll one of the dice. the new result total passss. player one then fails his charge and rerolls one dice and then also passes with the new total. both players have used their one reroll for this phase.
then player one rolls for winds of magic. he is ok with his total. but on the first spell he tries he miscasts, and chooses to reroll one of the 6's. he rolls another six, dang, still a miscast. player one then rolls for another spell, player two rolls to dispel and fails, chooses to reroll one of the dice and the new total is successful to dispell. both players have again used their one reroll this phase.
in the shooting phase player rolls for his catapult. one artillery and the scatter. he gets an 2 on the artillery and a scatter away from his target on the scatter. looking at the result he sees he could reroll the artillery dice and if he gets a 6 or higher he will still hit an enemy unit (just not the one he was aiming for) and if he rerolls the scatter he might hit his first target. he chooses to reroll the artillery dice and get an 8, hitting the different unit. player two has a character that gets hit, rolls his look out sir and fails, he chooses to reroll the look out sir and the new result passes.
etc etc etc.
#2 and #3 have been clarified by Raindog to be examples of what players might choose to reroll. NOT limitations of what can be rerolled. it is literally any one D6 per phase for EACH player.
hope this helps. (mr lucky makes for a LOT of rerolling)
however... it HASNT been clarified if mr lucky allows a player to reroll d6 while setting up the game (ie rolling to see who gets first turn). my assumption is no, as that is not occurring during a "phase".