I believe these type of leds are referred to as bi-color. Just be sure to limit the current to around 20mA max per I/O.

If the choice is between the AAA and watch batteries go with the AAA. They should provide more power thereby increasing your running time.

I would get away from the 16F84 and look at the 16F628A or 16F648A. There chips are cheaper, have at least double the capacity and I believe they even have an internal oscillator so you can use those extra I/O pins for some other function.