I know the life skill artifact Sethra’s Artifact can be found by selling imperial fish, imperial cooking/alchemy.  Is there any difference between selling all items in one click, or selling them one at a time?

Theres been ppl that have gotten more than 1 quest at the same time when selling multiple imperial boxes in 1 click. I dont think its confirmed however if you can have 2 quests with identical rewards at the same time. If you cant, selling the boxes 1 by 1 and turning in the quest as soon as you get it should give you slightly more chances at triggering the quest again.

I personally dont bother though. The quests have been so rare for me that its not worth the time or effort selling the boxes 1 by 1.

Maybe 1 by 1 is a little extreme, but smaller deliveries can be interesting. 

The chance is on each individual fish, so if you sell 20 at a time and you get it on the 10th fish, you won't proc the quest again on the last 10 fish.

Honestly, I'm just selling them all at once because most of the time I get enough fish that the trader will be full, so I hand in the quest, swap channels and deliver the rest.  I already got 3 artifacts that way.

I sell fish individually, and I never complete the flora lightstone until I get an artifact.  The Boxes I sell in batches of 40.