1) No. A band brings a character into battle. If the band is on a character, you can choose a different target next time they enter battle. If it's on an Enhancement, it's more intended to be one-use, although there are ways to recur them.
2) Yes, except it goes to your Land of Bondage, not Land of Redemption. Any time you draw cards, you put the Lost Souls in your Land of Bondage and replace them until you've got the specified number to add to your hand (or you run out of cards in your deck).
3) Abilities usually only last for the phase in which they activate - if Peter enters battle, he negates demons for that battle. In the next battle, demons are not negated unless Peter enters battle again.
4) Not really. Cards in your territory are more vulnerable than cards in your hand, and it lets your opponent know what you have.
5) Yes. Cards on/in other cards follow them in most instances. Weapons specifically follow the character unless it captured or rescued, in which case the weapon is discarded.
6 & 7) The I/J decks are trimmed down and don't have every card type. Sites are cards that have pyramid icons where there's the cross/Bible/dragon/skill, and you can put a Lost Soul in them to limit who can rescue them, as the brigade of the Site limits access to Heroes with that brigade (or otherwise have access). I think every healing Enhancement uses the word "heal", but I'm not certain.
Site:
As for Danites Attack, it takes a Site from your opponent (territory or battle) and puts it in your territory. The Lost Soul remains in their territory, and any other cards that had been placed on the Site are discarded.
Yes. A random shuffle leaves the possibility that no one draws Evil Characters.
9) A battle challenge is usually used to use your character's ability. Boaz's draw 1, Elders of the City's search, etc.
10) Unless a Dominant places itself somewhere, it is discarded after use.
