Interstellar Expansion. aka Enhanced Adaptation. Torians, Iconians have it too). This tech has no baring on story and it's description was written for multiple races.
It's also highly dependable on the biology of the race. Overall, I'm just not seeing it working for all races. For example, the Drengin are not known to adapt to other planets. They make other planets adapt to them instead.
Dark Influence. There's nothing there that states what the Korath do exactly so it could be stolen.
How can you use something, if you don't know how it works? The Korath most certainly won't tell you how to do it.
UnconventionalWarfare. Maybe?
It's intrinsic to the Drengin/Korath society. So I'd say, no.
OrganicMaterials. You could possibly steal this technology from another. Even the Iconians are just immitating the Precursors.
OrganicHulls. Ditto
SelfHealingHulls. And ditto
I consider those major features of the Iconians. They are the ones with the Precursor-techs. If everyone can get them, then what makes the Iconians unique?
Considering the Thalans moved to out dimension and are using currently available fusionreactors to do everything it is reasonable to assume other space faring being could understand these techs.
I don't think so. The parts may all be contemporary, but the items themselves are based on scientific knowledge that is way ahead of ours.
Cut-Throat Competition
Super Trade Starbases
No, to both of these. Both are major features of the Korx. Plus, the Super Trade SB module requires the Protection Racket module, which gets unlocked by Fortified Freighters.
Xeno Refining*
Expert Refining*
Starbase Victory Strategy*
Starbase Supremacy*
I don't think the Korx would trade such huge advantages away. They may love making money, but they are not stupid.
I would also add the following techs to the mix of possible candidates to steal:
Robust Hull Construction
Hull Strengthening
Creative Good
Paradise Worlds
Righteous Might
Righteous Justice
Fleet Warp Bubbles (I forgot to set these to un-tradeable/stealable earlier.)
Fleet Warp Bubbles II
Fleet Warp Bubbles III
Anyhow, I've run a few tests with the remaining races:
The Torians are doing okay overall. However, they often lack the space to build Healing Pools on Toria and other planets, because it is used up for Schools. This is pretty bad for approval, especially if the Torians built a Harvester on Toria (which often isn't the case, due to the same problem).
The Arceans and Korx haven't researched Xeno Engineering and/or Planetary Improvements several times. Also, in one game, the homeworld of the Korx looked like this in the middle of 2229:

In case you're wondering, no, the planet hadn't been conquered or culture-flipped. The Korx were far off in a corner, where no-one could reach them.
The Drath aren't researching Temples, and often don't research beyond Xeno Mysticism. In the last couple games, they haven't even researched Xeno Mysticism itself. Even when they had a good start. They do, however, have no problem going for War Profiteering (and abusing the hell out of it).
I'm not quite certain about the Thalan yet. They do seem okay, but I have the suspicion that they did better on AIP 8. That may, however, just be my imagination. I'll keep an eye on them though.
The Korath don't research Spore Weapons. At least, they didn't in any of the test-games today. It's strange though, because I had them reliably research Spore before, even when their start sucked. Maybe it is due to the bigger map, or one of the other settings. Weird.
The Krynn do okay, but they sometimes neglect Planetary Improvements in favour of their influence techs.
I think that's all of the races now.