Electronic – arduino – Netduino/Arduino to Variable Resistor

You are going to want to use a linear regulator. This will be very inefficient with respect to power efficiency, but your arduino should not use much power and this should make the power point moot.

Here is an example search for the part you would need on mouser. If you are going to pull very much current you are going to need a heatsink, this would probably amount to anything greater than 100mA in your case(just a ballpark so you have a way to estimate your threshhold).

It will require a couple of capacitors, but any good datasheet will tell you exactly what components you need.

Using only one resistor for 6 LEDs is not a good idea: if there's a slight difference in forward voltage between two LEDs one will light brighter than the other one.

edit
Splitting the 6 LEDs in two groups of 3 and using additional inputs of the ULN2803A would only help if you would exceed the maximum current for one driver. But each driver of the ULN2803A can sink 500 mA, while 6 LEDs will need only 120 mA.