Am I correct in that it would be completely pointless for me to use both an optocoupler and a transistor in driving the relays, given that I am using the exact same 12V power supply to power both the Arduino and the relay coils? Or is there some added benefit to using an optocoupler in my application that I’m missing?
I can't see any need or advantage to using opto-isolators, from what you describe.
A slightly more sensible arrangement would have been a 5V PSU and relays with 5V coils. You would then bypass the Arduino's internal regulator, powering it through the 5V pin instead of the Vin pin or barrel socket. But if you already have the 12V relays or power supply, then go with that. Just take care not to draw much current from the 5V pin of the Arduino, the onboard regulator can easily overheat with a 12V input.
Yes, as long as your phone charger is rated for enough current. Most Arduino only use 30~50mA, but relay coils can be 100mA each (usually less).
Best to avoid reverse polarity by using a connector that can't be reversed, like usb. Barrel plugs & sockets are usually centre positive but they can be centre negative, especially if you buy one of those universal PSU with 10+ adapters for different size barrel plugs. If you rotate the adapters 180 degrees, they can be made centre negative.
