Make LUFA for Arduino UNO / atmega16u2
As per my comment, you have specified UNO board, but it doesn't have Keyboard/Joystick required definitions for the board (I'm not sure if UNO has any buttons to be defined there, it only has Leds, and leds are defined in Led.h - check out \LUFA-111009\LUFA\Drivers\Board\AVR8\UNO)

So what you could do is to create Board folder under your KeyboardMouse and make empty files Joystick.h and Buttons.h there. This should get you going further. Errors you are seeing are due to the following code in \LUFA\Drivers\Board\Buttons.h

#if (BOARD == BOARD_NONE)
    #error The Board Buttons driver cannot be used if the makefile BOARD option is not set.
#elif (BOARD == BOARD_USBKEY)
    #include "AVR8/USBKEY/Buttons.h"
....
#else
    #include "Board/Buttons.h" &lt;------ THIS IS EXECUTED SINCE UNO DOES NOT HAVE BUTTONS
#endif


So your error 


  ../../../../LUFA/Drivers/Board/Joystick.h:119:31: error:
  Board/Joystick.h: No such file or directory


means that your folder structure and your LUFA configuration is correct, but you're missing file Buttons.h in your KeyboardMouse/Board/ folder. Got it?

Try what I've suggested and see how far you get. You can see how to define buttons in other Board's folders, for example in LUFA\Drivers\Board\AVR8\USBKEY\

EDIT
Btw, I forgot to mention, error about common.h should go away hopefully after fixing this since that ........\ is coming from a file in a different location in folder structure thus confusion.

EDIT
OK, so here's the link on how to build custom board drivers:
http://www.fourwalledcubicle.com/files/LUFA/Doc/111009/html/page_writing_board_drivers.html

What you need to do is to copy files Buttons.h and Joystick.h LUFA\CodeTemplates\DriverStubs\ (or try copying Buttons.h and Joystick.h from USBKEY better, I think you still would need to specify a value for each definition otherwise) This should get rid of undefined errors. You have TODO sections in the files that you need to update.

OK, so I think I should also mention how this is supposed to be used before going further. These drivers/definitions are meant to be used in a specific manner in your code, and LUFA is unifying the approach for you. As far as I can tell, buttons are used in a following manner:

if (Buttons_GetStatus() &amp; BUTTONS_BUTTON1){ ... do something when button 1 pressed....


This way, if you have several boards with at least one button, your code should theoretically stay the same across the boards.
Similar stands for LEDs, you can use them like:

LEDs_SetAllLEDs(LEDMASK_USB_NOTREADY);
....
LEDs_SetAllLEDs(LEDMASK_USB_ENUMERATING);


I hope you get the picture. In order to use these library functions you have to define buttons/joystick/led specifics in their respective header files. So for example - in buttons.h you need to specify any custom header files you need, add port masks for buttons (on which pin of which port they are connected), specify port initialization and how to read the status of the buttons. You can find all of that in the USBKEY's buttons.h - e.g. it's importing common.h, defines BUTTONS_BUTTON1 like pin 2 of a port, initializes PortE with this button (so button is pin 2 on port E), and in Buttons_GetStatus it reads the status of the button.

I could go on and on in the same manner for joystick as well, but I hope you get the picture. Joystick is more involved but it's like having 4 buttons of which 0, 1 or 2 can be active at any time.

BTW, this is only useful if you have any buttons on your board. For example, I made keyboard driver without any buttons (I had to remove buttons specific code though). I used Ir Diode to read remote control codes and make the board act as keyboard. So you don't really need the buttons, nor the joystick (of course, it completely depends on what you're doing).