Can we Change thin in "Nose left" and "Nose right"?
There's no need to change this, since the indication of where the Nose will go it's already there in the message.
The Airplane can never go backwards itself, so the Tail direction makes no sense for me.
The indication doesn't have any relationship to the direction the airplane is moving. It's only meant to describe the final position the airplane will be at the end of the pushback.
The GSX indication is made like that, in order to suit BOTH users accustomed to the FSX default standard of referring to Left/Right as being the direction the tail will go AND users accustomed to the standard of Left/Right being the airplane facing, so the message clearly indicates both, in order to make it impossible to both kind of users to misunderstand it.
