1. You're reasoning on the current is incorrect. The current is determined by the voltage and the resistance. Your 2A rating on the battery is the MAXIMUM current it will supply. But, with 12V and say, a 1K resistor, it would actually be only supplying 12mA. Think of it the 2A rating as max allowable current, not actual current. V=IR is your friend.

2. See (1) above. Yes, there will be less current drawn when only displaying 2 instead of 7 segments. But, each segment should have a current limiting resistor, normally limiting to around 15mA. In your case, worst case is with all 264 LEDS on, which gives max power per led of 7.5mA with your 2A supply. You won't have them all on at the same time, and certainly not for very long, so you could probably go with about 10mA per LED. Therefore, for your 12V/2A supply I would suggest a 1.2KOhm resistor in series with each of the LEDS. That's the basic theory, but it also depends on the driver chip you end up using and the way you connect up the LEDS.