aquinas - your first story reminded me of our family's "opposite-bot" game which was started around that age and the kids still love to do.

An opposite-bot is a robot that does the exact opposite of what you tell it to do. In our house it generally ends up in loops like this -
In your best robotic voice - "I am an opposite-bot"
"If you are an opposite-bot and you say that you are an opposite-bot then that means the opposite so you are not an opposite-bot but if you aren't an opposite-bot and you say that you are then that means you are...." and so on.

I recall some odd looks when the game devolved to this in the checkout lane and the kids were 4 and 2....