I know machine sprites can use the Diagnose power to add dice to pools that involve the use of a tool. How far does this go?

Can a machine sprite use this power on a commlink to give a hacker dice to all hacking?

Can one sprite use diagnose on a gun, while another uses it on a smartlink system, and do the bonus dice stack in this scenario?

Don't realy know on the first question, but when it comes to machine sprites helping your shooting I would have to say no. The smartlink is no auto aim, it is still you that is aiming the gun. If I have inderstood the smartlink weapon accesory it just creates something like a FPS HUD for you so that you can aim easier.(And know everything else that you need about your gun.)

It can add bonus dice to the gun but not using the commlink for hacking. The gun can be enhanced by the diagnosting of "small errors" by the sprite and telling the user "if you pitch it a little bit up you can shoot better".
The machine sprite is more of a "for the real world stuff" sprite than anything else, so this would be my personal take on it.