Answers: (By the way, the Axis is a Savage. )

1) Is the action as stiff as a Savage? I don't know, it may be stiffer ?

I could hazard a guess that it is stiffer due to the solid top and side, but in real life, for me it does not make a discernible difference.

2) Does it use the same barrel nut as a Savage ?

Yes. Small shank barrel nuts will fit the Axis.

3) Will Savage after market barrels fit a Axis ?

Savage Small shank barrels will fit nicely.

4) Can the trigger be as finely set as a Savage, can a used Accu-Trigger be installed ?

The trigger can be worked on and I have set mine to be as good (IMHO) as the non-accutrigger savage trigger. It will not be the equal the older three-screw trigger nor the accutrigger.
With some slight modification, an accutrigger can be installed in an Axis. Check here for more information.

5) The action is one length, is there a built in stop for shorter cartridges or does the bolt go all the way back as a long action stroke ?

On my .223 Axis, the bolt goes all the way back. I would guess that an extended front baffle could be used to limit rearward bolt travel, but this is supposition, not fact, as I have not tried it.

6) Is there any accuracy differences between the two actions ?

I do not know if there is an inherent accuracy difference, but if there is, in real life, for me it does not make a discernible difference.