so for section one use one resistor per two LED's
No No No.
No apostrophe needed in LEDs but more importantly you need one resistor on each LED because LEDs in parallel do not share current equally.
The reason you need a resistor is that the LED usually can't handle the power (voltage X current) the digital pins provides to it.
No it is the current not the power, LEDs are a non linear device and do not obey ohms law.
The value of the resistor depends on the LED you are using, you can easily calculate it by looking up the max power of the LED and the current and voltage output of the digital pins.
That is not a quality answer.
The total current from one Arduino output pin should not exceed 30mA, anything over 40mA damages the processor. So you can't run two LEDs from one pin @ 20mA each. Anyway that would probably be too bright to look at directly so calculate the resistor for a 10mA current.
However before you can calculate the resistor you need to know the forward voltage drop of the LED, if you don't have a data sheet you will have to measure it.