No need to apologize.How much current do you wish to flow in the LEDs? If more than 20mA per LED, or if they add up to close to 200mA at a time, you'll need to use driver transistors.What is the rated voltage drop across the LEDs you are using?If no more than 20mA per LED and you never plan on having all 10 on at a time, use Ohm's Law and the difference between Vcc and the LED rated forward voltage to calculate the resistor value.R = (Vcc - Vled)/II have some Green LEDs here that drop about 2V at 20mA. That would be:R = (5V - 2V)/0.020AR = 150 ohmsAs for the Arduino power draw, it is greater than what just the microcontroller draws because of the support circuitry. I'm sure Grumpy_Mike is right about that, and as he says look to the Datasheet for the XBee module.What 5V battery are you using? I don't know of any batteries putting out 5V. However, I have successfully powered a few Arduinos from 4 AA NiMH cells, which together add up to 5V fully charged and about 4.8V for most of the charge.
You can also refer back to the Arduino cookbook Chapter 7, it shows you how to design and choose the correct resistors for powering LEDs
Is it then possible to calculate how long my 9V battery will last?