Calvin and I both have 7s showing, and 1 card left in our hand. When I click the 1 card, nothing happens and the same screen keeps coming up. Am I just supposed to quit the game?

The same thing happened to me and I couldn't figure out what to do so I just quit the game. If you've only got one card left, it probably means you've lost (in case of ties, it's decided by suits...I think)