Technically, you could light up all the LEDs at one time, but that isnt how the software usually works. Usually you light up one led, or you light up the leds on a plane at one time, but that isnt true of all cubes. For your 3x3x3 cube, you will likely light up between 0 and 9 LEDs at a time. using up to 180mA at a time. each LED has a 33% duty cycle.
You probably want the 150 ohm resistors, but the only problem with using 220 ohm resistors is that they wont be as bright, so it will still work, and the LEDs will last longer at 220 ohms, but it may be insignificant. People using 220 ohm resistors maybe using LEDs with lower forward voltages, red are usually very low.
I think Its possible to do all the other things you list, but you probably wont want to do them.