Desktop with Windows 7 <=>
USB <=>
Arduino UNO
This I assume is just the standard programming/download cable for the Arduino, so not actually a MIDI connection.
Arduino UNO <=>
Breadboard Wiring <=>
Midi Jack
This is the circuit, so the MIDI message generation component and circuitry for the interface
Midi Jack <=>
MIDI to USB cable <=>
Micro USB otg cable <=>
Nexus 7 <=>
Grand Piano pro version (supports Midi via USB)
This is the component that sends the MIDI messages.
The MIDI/USB cable has two ends - you should be connecting the 'OUT' side (labelled on the plug, usually) and LEDs - do they light up when you are sending messages? If you can't see lights, your circuitry/software is not working as expected. The USB converter cable should have no effect and seems to work given your comment previously.
If you are seeing the LEDs on the cable, then it is probably in the configuration of the software receiving the message.