If my Leader's type includes "Whitebeard Pirates" but I have no Life cards or any Life cards to add to my hand, can I play this card?
Yes, you can. In this case, you can use the [On Play] effect to lower the power of 1 of your opponent's Characters, but you will not be able to add a Life card to your hand.
My Leader is a Leader with the type "Whitebeard Pirates". If this Character's [On Play] effect does not give 1 of my opponent's Characters −2000 power, can I choose not to add 1 card from the top of my Life cards to my hand?
No, you cannot. Even if you do not give 1 of your opponent's Characters −2000 power, you must add 1 card from your Life cards to your hand if possible.