What happens if I have one card left and my opponent has one card left and I attack him and he successfully beats my card?

That is a draw. If you attacked with your last card(s) and the defender beat your card(s) with his last card, you are both successfully out and it is a draw.

What if I'm out of cards during a round and then there are no more cards in the draw pile when it's my turn to refresh?

You are successfully out of the game because you got rid of all your cards and there are no more cards to draw.

When we're playing the Ruthless Version, and I want to pass three cards to the next player but he only has one card, can I do that?

No, this pass is illegal because you cannot attack with more cards than the defender has. EXAMPLE: You are attacked with a blue King, you have a red King so you put it down to pass both cards on to the next player, but that player only has one card. You cannot pass the cards because you cannot pass two cards to a player with less than two cards.

When we're playing the Ruthless Version with two players, can I pass cards back to the other player?

Yes. Let's say you attack with a red Knight and the other player has a blue Knight, she can pass both cards back to you to defend. If you had a green Knight, you can pass the three cards back to her to defend and so on.

When playing the Ruthless Version, let's say I'm attacked with a blue Queen, and I have a green Queen which is the trump color, do I have to pass the cards or can I just beat it?

You can pass the cards or you can beat it. It's up to you.

Can we play Game of Kingdoms with more than 6 players?

Yes, just combine two decks and you can play up to 12 players.