- To convert the electrical power in the car (12V with 370 CCA) in order to safely power my Arduino UNO
The Arduino has an on-board regulator and it's rated form 6-20V (7-12V recommended). The "12V" in a car is nominally 14.4V and you can get voltage spikes, so some people use an external voltage regulator such as an LM7805 (bypassing the built-in regulator).
But, I've done something similar (sound activated lighting) and I just power the Ardfuino directly from the car power. If you are powering other things through the Arduino's voltage regulator you need to be "more careful" because the heat dissipated by the regulator is a combination of the voltage dropped across it and the current through it. (Power = Voltage x Current).
- To convert the same power in the car (12V with 370 CCA) and use it to power my designs, which has a power consumption of 24V, rated at 700 mA.
You'll need a step-up DC-DC converter rated for 700mA or more. Give yourself some safety margin and get one rated for at least 1A. (This will "pull" a little more than twice the current from the 12V side.)
- To use a MOSFET transistor, whose gate pin is connected to the UNO, in order to toggle the design on/off rather quickly.
[u]Here is a MOSFET driver circuit[/u]. Note that it switches the "ground side", which is easier with a transistor or MOSFET. That shouldn't be an issue with LEDs/lights but it may not be convenient with other things. (If you are powering lights or another non-inductive load you can leave-out the diode.)
Or, a solid state relay can be used to switch the power-side or ground-side. Just be sure to get one that can be controlled by 5V, and one that's designed to switch DC at the required current. (Most AC solid state relays will latch-on and never turn-off with DC.)
The Arduino will take inputs from a sound sensor
It's usually better if you can tap-into a line-level signal (i.e. the signal from your head unit into a power amp), rather than picking-up ambient sounds. Speaker outputs can work, but you'll need a protection circuit and probably a voltage divider to make the signal safe for the Arduino.
Even with a line-level signal you'll need to bias or protect the input because the Arduino can be damaged by the negative-half of the AC audio signal. (The standard/common Arduino microphone boards have biased outputs that put-out about 2.5VDC with silence.)
and use that to power a light display inside. Therefore I will create a sound-reactive light show.
I'm sure you have a design in mind, but you can do "amazing things" with [u]NeoPixels[/u] (or DotStars) and you don't need a driver circuit. Just a power supply and a signal from the Arduino. DotStars require two signal wires, but the programming/timing is easier. (There are NeoPixel libraries so the hard part of the coding is already done.)
I didn't use either of these in my project but I'm thinking about an "upgrade" at some point.