Chicken On Your Head and Justice Pie questions

[Bimbelton]

First question: Curse! Chicken On Your Head!

The card says that "...Any Curse or Bad Stuff that removes your Headgear will take the chicken with it." -- Am I correct in interpreting that if you do not have headgear this Curse does not effect you?

Second question: Justice Pie

The card states that a curser, or anyone who played a card against you in a combat must discard two cards. -- Can cards that are being carried be discarded to satisfy this situation or any other situation that tells you to discard cards?

Thank you!