New Redemption Grab Bag now includes an assortment of 500 cards from five (5) different expansion sets. Available at Cactus website.
First answer is no. Second answer is yes and no. There is a difference between hopper/revealer and site-remover. Hopper and Revealer only work when drawn whereas the Site-remover works when it is placed in your Land of Bondage so the ability would activate if you search for it.
Most cards that search for a lost soul is an opponent's card. If they "draw" a lost soul from your deck, then it wouldn't make since for them to "draw" another card.
Each time you draw a Lost Soul at any time in the game, it is immediately placed in your Land of Bondage and replaced by drawing another card.
A search card can be played to get a Lost Soul from your draw pile. If this is done, you must put the Lost Soul in your Land of Bondage, then shuffle your deck.
I am talking about using search or False peace to search my own draw pile for a LS and then placing it in territory and immediatley drawing a replacement card from my own deck. I have done that before. especially searching for the Color guard LS.