-Uses only a chip(without the arduino board)I wanted to get my costs down and made a standalone board using only the chip.
6 PWM pins neededYes
-The LEDs and resistors are soldered onto pre-printed circuit chipboardsIf you mean a manufactured PCB, then yes this is possible, but you have to design it and they can be pricey. I like using Adafruit proto boards as they are nicer than regular perf boards. https://www.adafruit.com/products/571