From what I understand, Player 1 draws a Barking Kitten, they have to place it face up right in front of them until another player draws the second Barking Kitten (hence there are two Barking Kitten cards). Player 2 draws the second Barking Kitten,Player 1 then has to give half of their hand to Player 2, in return Player 2 will give the same amount of cards back to Player 1. So if Player 1 has four cards in their hand they will have to give Player 2 two cards, while Player 2 also has to give two cards back to Player 1, so if Player 2 has eight cards they will still need to give two cards back to Player 1.

As for the Tower of Power, I do not know how it works I am also confused on how it works.