1. You can vary both the on and off time, but you'd need two pots to adjust them both.
2. Yeah.
Go to Iguana Labs, this page shows you how to use and calculate the on and off times using two resistors.
When fading the LEDs, put the cap on a transistor's base and drive the leds off that. That way you can use a much smaller cap. When choosing the value of the cap, I'd put the 555 at a very slow frequency, so you will be able to see the full charge and discharge cycle of the cap.