Tell us about yourself!
I used standard equipment wire. I normally use www.esr.co.uk as they're pretty good on prices. The unit only draws minimal current, so any cable capable of carrying 1A is more than over specified.
No, that's me! I've been working with them for the past few months on it. Glad you've seen it.
It runs on a standard USB connection. It'll work off 5v @ 500mA - a standard iPhone charger. I believe that the code from Adafruit multiplexes the LEDs, so they're not all on at once, they just look like it. You are right however, 128 LEDs @ 20mA each equals about 2.5A, so yes it would then draw a lot of power.
Which part of the programming are you having difficulty with?