Circuit: Breadboard, wires, Arduino Nano, 2004 LCD screen, 10kΩ potentiometer, PL9823 LED.
The PL9823 is Neopixel-compatible. You will need to install the Neopixel library: https://learn.adafruit.com/adafruit-neopixel-uberguide/arduino-library-installation
To connect the LCD screen correctly, see the tutorial over at Arduino.cc: https://www.arduino.cc/en/Tutorial/HelloWorld (I have changed the pin numbers used, read the code...)
The HC-05 TX pin on the left is connected to the Arduino's RX pin; it acts as a 9600 baud serial port.
For the Android part, install one of the HC-05 controller apps on your phone. This one seems nice: https://play.google.com/store/apps/details?id=com.mightyit.gops.bluetoothcontroller
Supported commands which you can send over bluetooth or serial:
/R127: Set the red component of the LED colour to 127
/G127: Set the green component of the LED colour to 127
/B127: Set the blue component of the LED colour to 127
/f84: Display the specified 3-digit hexadecimal colour
(the three digits are R, G, B respectively, and f(15) is the maximum)
/clear: Clear the LCD dsplay
/funky: Change into "funky" mode, which cycles through white, primary and secondary colours
Any other text (without a / in front) is displayed on the screen.
The Arduino will wrap text over 20 characters onto multiple lines.