there are resistors for the leds, just beside the leds. you don't need any resistor, just unsoldier the leds you need, and solder another led.
there is a voltage regulator on the red w5100 modules, an AMS1117@3.3V, so you can feed them from 4.3v to 15v
it needs 3 AAA batteries, or a 9v battery ? or some dual li-ion module battery ?
when all the leds are on, it consumes around 200mA @ 5V