Some doubts on very basic rules!

[mqstout]

1: Abilities on a hero only work for that hero, unless otherwise stated (Father Joe's cancel).
2: You cannot. Once dice are rolled, the card has taken effect and it's too late to cancel. If it was a "remains in play" card, you can cancel it still -- but any other things it may have done (such as filling a building with zombies) will not go away; just the taken over market.
3: Unless otherwise stated, you roll dice first and then choose to add Combat Bonuses as you desire. But, in your example, once you've used the cleaver, it's in for the combat even after you've rerolled. Once you've decided to use the Combat Bonus, the weapon's counted as used for the Fight.