Using Arduino as ISP — Not able to programme anything

THis line right here has teh problem -

avrdude: Device signature = 0x1e950f
avrdude: Expected signature for AT90USB82 is 1E 93 82

AVR is expecting to get an ID response back of 1E 93 82 and your chip is responding 1E 95 0F.

If you are sure you have everything setup correctly and this is just a newer version of the chip you could add -F to your command telling AVRDudue to ignore the signature and program anyway. It looks like its there...

What version of Arduino IDE did you use to load the ArduinoISP sketch? if you did it with 1.0 there is a bug. Load the ArduinoISP sketch using 0.22 or 0.23. With Arduino-1.0 the ArduinoISP sketch only works at 9600 baud.