Can u parry an Improved Parry (out of turn incidental attack)? For example I hit an opponent with 10 damage. They have soak 3 And the rest of it they parry and then use improved parry which allows them to after parrying hit me with base damage of their weapon (let's say it 7). Could I then use parry on that? And also does that improved parry damage ignore my soak?

For your first question, to my recollection (away from book) you can Parry a bit inflicted by Improved Parry. The Parry talent is "one hit" and Improved Parry inflicts "one hit."

For the second question, no, it does not ignore soak. It's treated as a regular hit and thus gets affected by Soak.

A lightsaber improved parry isn't still lightsaber damage that has breach?

I know improved reflect is base damage of the energy weapon, but don't see that improved parry is not the actual lightsaber.

Improved parry only has breach if the weapon one is using has breach. IE an improved parry by someone using a ancient sword does not have breach.

Yes, you can use Parry in response to a hit generated by the Improved Parry talent. This was actually confirmed in a Twitter conversation between a couple of FFG staff from their own Force and Destiny game with Parry and Improved Parry being activated multiple times in the course of a single combat round.

Note however that you can't trigger improved parry from improved parry. There is no dice roll on the improved parry hit to produce the despair or threat needed.

Note however that you can't trigger improved parry from improved parry. There is no dice roll on the improved parry hit to produce the despair or threat needed.

I know it's not official, but I would allow you to improved parry an improved parry. If your opponent parried you using a Despair and you had net 3 Advantage (or a Triumph), I'd let you use those to get in a new hit with improved parry.

Yes, I know Advantage/Triumph are normally spent before Threat/Despair, but it's so narratively compelling I'd allow it. And of course your opponent is likely to parry you again, but then you're forcing them to take more strain, so it's still a slight gain for you.