Yes, you need a relay board (or transistor or MOSFET, etc.). As you probably know, a relay is an electrically controlled switch.... You are replacing a switch with a switch, so t that's the "safest" solution.
But if there is no controller with unknown electronics and you just have to switch 12V power, a MOSFET is pretty "safe" too. (MOSFETs tend to make better power-switches than transistors, so let's forget about transistors.)
The Arduino chip* runs on 5V, so the digital I/O pins are +5V when high. Also, you can't put more than 5V into an input-pin.
And, the "absolute maximum" current from an I/O pin is 40mA, so you can't directly power much more than a standard LED.
I've never used bluetooth.
Is this something that is not worth doing?
:D Of course it's NOT worth doing! :D No NORMAL person is going to add LEDs and color changing halos and glass-in a custom gauge display! It' too much work and too costly, and nobody is going to pay extra for it if you sell the car. :D
....My van came with "mood lights" in the ceiling. My sister was telling someone that I had added them. I said, "No, if had put them in they'd blink to the music." So, after a couple of months of thinking about it, and a couple of months of design, programming, and re-wiring, the lights "dance to the music" with several different flashing/filckering/sequencing modes. Was it worth it??? I'm impressed! I think it's cool! But, it's behind me, so I can't see it very well when I'm driving. And, I mostly just use the van for vacations & picnics. If I show it to someone they might be amused for about 15 seconds... Nobody REALLY appreciates it but me! Nobody cares about all of the random modes & variations I programmed-in that keep me from getting bored with it. But, I'd do it again!
BTW - I used solid state relays which can be a little trickier to choose than standard relays, but they are faster and they don't "click". I could have used MOSFETs... That' just one of those choices you get to make when you design something.
- The Arduino board has a voltage regulator so it can run off 12V. Some people worry about voltage spikes in the vehicle's electrical system, the Arduino in my van is working fine with the on-board regulator.