However I plan on using 3.0 - 3.2v 0805 SMD LED's, and require two for each warning light.
The question is, can I wire the two LED's in series, and do away with the resistor?
Well, it might work. Two 3.0 V LEDs in series would obviously require 6 V and you should always provide current limiting. it is possible that they will in fact light on only 2.5 V each and will then limit their current draw by their own internal "resistance". I suppose you could try it out, but I doubt it would be satisfactory. Better in parallel with a 470 Ohm current limiting resistor for each
Additionally, as there will be 12 warning light outputs per Arduino (I was thinking of using Nanos) would it be best to put a 12v power supply to the VIN pin?
You need to understand something basic about Arduino boards.
The on-board regulator is absolutely not provided to power external equipment. The exception may be sensors which require only a few milliamps to power, and a few indicator LEDs at 20 mA each (with a current limiting resistor).
No motors, no LED strips, no relays or solenoids. The USB input is able only to supply just a little more current.
To power these things at 5 V, provide a proper power supply. Almost always this means a regulated switchmode mains power supply (such as a "plug pack") or "buck" regulator from a supply such as a car battery.