That are many questions, and each problem has a number of solutions.
Perhaps you might need to drop some features, to be able to finish the project.
Arduino : It is best to start with Arduino Uno. That is the most common Arduino Board.http://www.arduino.cc/en/Main/arduinoBoardUno
If you get to know the Arduino Uno, you can decide where to go next.
Using a mosfet or transistor to switch leds is not hard.
Using a battery (for example a Li-ion battery), perhaps with a DC-DC converter is possible.
Audio processing with the Arduino Uno is possible with some Audio/Sound/Voice shield.
Wifi is also possible with the Arduino Uno, with a Wifi Shield.http://arduino.cc/en/Main/ArduinoWiFiShield
But an Arduino Uno with a Wifi shield and a Voice shield and output stages makes it complicated.
I don't know the XBee boards, but perhaps such a board with wifi is a better choice. I think it is Arduino compatible.