|[Is] "GENIUNE" windows 8 running on windows tablets is exactly the same as the windows 8 running on desktops/laptops|
Yes - there is no distinct tablet version of Windows 8
(There was a tablet specific edition for Windows XP -- Windows XP Tablet -- but not for more recent versions of Windows)
|Is it possible to code c++ on a tablet?|
As the desktop is available it is possible, but it would be rather cramped for serious development work. Most people would prefer to develop on desktop PC and then copy binaries on the tablet for testing, etc. (Or even write an installer.)
Also, there's nothing to stop you plugging a mouse or keyboard into tablet (if they all have enough USB ports). And some tablets even allow you to plug in an external monitor.
(Due to the lack of screen space on a tablet, a lot of people even use a remote debugger to diagnose problems on a tablet, so you can actually see what's going on. Also see comment about mice, etc further down.)
|Can you incorporate libraries in the same way?|
Yes (DLLs and static libraries are just the same as they ever were)
|Is there any difference at all aside from the virtual keyboard and touchscreen in place of the mouse?|
Nope -- With the caveat that the functionality available will depend on the hardware.