Electronics noob here. I've spent like 5 hours researching and I think this works.
I want to install an LED strip in a 20 ft. enclosed trailer I use for work. So far I think I have everything picked out.

LED LIGHT STRIP connected with THIS ADAPTER to THIS LED DRIVER. Finally, THIS PWM would regulate it all.

The LEDs are 3.5W per Ft. so that makes the whole thing 56W at 12V power from the truck battery. Which means it will be using 4.6A. (which means 276 mAh right? so a battery with 780 cold cranking amps should run it for roughly 2 hours right?)

Questions: Do I really need that LED Driver? My impression is that its basically a capacitor to smooth out the power from the PWM. I have no idea really, my brain is kinda cooked.

 

I think you are overthinking this. If these lights are made to run on 12V, you should be able to just hook them up to the vehicle battery directly. Not sure what the ampere hour rating on your battery would be, but it will determine how long they can run before you run into trouble. It's that simple.
The Adaptor, driver etc is for use in a setting where DC voltage has to be converted from and AC source. This is not the case.
LED strips do not use much current so they should run for hours without too much drain on the battery.

 

Ah. ok. What about the PWM? I learned that its a much more efficient way to regulate power compared to a potentiometer. I definitely want the car to start after I'm working in the trailer. Is it the appropriate one for the lights?

I think you are overthinking this. If these lights are made to run on 12V, you should be able to just hook them up to the vehicle battery directly. Not sure what the ampere hour rating on your battery would be, but it will determine how long they can run before you run into trouble. It's that simple.
The Adaptor, driver etc is for use in a setting where DC voltage has to be converted from and AC source. This is not the case.
LED strips do not use much current so they should run for hours without too much drain on the battery.

 

PWM is an efficient way to dim the LEDs but if you just want them on or off, you don't need a dimmer and don't need PWM.

 

+1 wayneh. If you are concerned about working for long periods of time and running the battery down, you may want to consider a deep cycle battery as a house battery and tie it in with a magnetic switch. You can run off the deep cycle for as long as it will provide power, and never affect the vehicle battery. This is better money spent.
As for PWM, as said earlier, it would be used for dimming control and is very good at it in comparison to a Potentiometer.
I guess the cheap route would be to add a second battery in parallel to give you more capacity. If this is a tow unit or diesel, I would think it should already be set up that way.