VGA input cannot be compared to RCA, to demonstrate that, try typing a word document on a standard TV. You can't read anything below 16pt font usually.
I believe most LCDs use 12vdc, the backlights run on 12v (use an inverter to get it to their proper voltage) and then the LCD doesn't need any other external power.
Some LCDs use an AC adaptor because they were meant for home usage (Datalux come to mind, I believe).
I've got a 10.4 I was looking to sell, 18bit color 800x600 res, it's a touchscreen around 250nit I was asking $350 shipped.