Welcome to the Official Redemption® Message Board!
1. "Pending abilities" don't really exist in Redemption. There are ongoing abilities, like protection, but everything else is instant. When you remove a character from battle that technically happens instantly and the character is removed. Special Initiative is a mechanic to allow the removed character to interrupt/negate their removal it doesn't cause any abilities to be "pending."
1. If AotL (or a "cannot be negated/interrupted" card is played) yes, but if you have special initiative you cannot use those cards since they don't interrupt or negate.
1. If you pass on special initiative (or have no cards you can play to stop the card removing you), you still get a period of time if you wish to use a Dominant or artifact before battle resolution begins. Both players must pass on playing any further cards before battle resolution begins.