For a card to be considered an "opponent's card", that player must be the owner of the card as well as have control of the card.
Since you are controlling the Hero on your side of the battle, it's ability would not be negated by CoM but the Hero on your opponent's side would be.
No, the EC does not get SI because it is not in the current battle. If the Evil Character is removed from the main battle, then when you return to the main battle it resolves as any other unblocked battle does: if a Hero is in battle, they win barring any Dominant intervention.