If the SA of a card has an effect (say an underdeck effect) that removes my opponent’s lone character from battle AND another effect that brings a card into battle on my side (say a band or equip effect), (1) does the second effect on the card get to activate before my opponent gets SI and if so (2) does the SA of the card added to battle then get to activate as well before my opponent gets SI?
For example, I block my opponent's lone hero with The Rabshakeh (LoC) who says, "If blocking, underdeck a good card. Opponent may reveal hand instead. You may equip an evil weapon from Reserve or take a pale green enhancment from Reserve. CBP" Suppose my opponent must negate The Rabshakeh because his hand is protected and suppose I wish to equip Hired Sword (LoC) from my Reserve.
Hired Sword (LoC): "Negate an opponent's card. Opponent may discard the negated card. If they do, discard this card after battle. If they do not, you may draw 1."