QCan a card that has the Cute, Cool, and Passion traits satisfy abilities that only mention one of those traits, such as "select a Cool follower in your cemetery and summon it"?

AYes, it can.

QCan I banish 3 cards that each have the Cute, Cool, and Passion traits, such as New Wave, as part of this card's additional cost to play it for 9 less play points?

ANo. A card with all three traits will only count as one card. It may be counted towards any of the trait cards, but you will still need to banish a total of nine cards, three from each trait, to pay the additional cost.