Ambilight - Arduino Uno with WS2812B

I'm planning on building an ambilight system using the Uno I just purchased. The issue I see is the Arduino website says I can only use a 9-12V supply for the Uno but the lights take 5V and on all the tutorials people are using 5V 10A DC adapters. Can I use a 5v 10A adapter for this project?

Yes. The simplest is to get a USB phone charger and plug it into the Arduino USB connector. You can connect 5V to the 5V pins of the Arduino if there is no other power source.

I believe I'll be using the USB connection for ambilight to send the pixel information from the computer to the Arduino. Could I use a 10V DC adapter instead that the Arduino would transform to 5V for the lights?

If it is plugged into a computer won't it get power over the USB cable?

If you are using an Uno, Mega or other board that has the voltage regulator on board then, yes, you can use a DC adapter of the appropriate voltage to power the board.