My comments/suggestions on the Super Abilities:
It is my current belief that Super Abilities *should* be super powerful. The trick is making sure each super ability is just as powerful, but in a different way.
Super Diplomat/Manipulator - These two are not only too similar, but they are very hard to quantify just how much benefit they give. The trading screen should clearly indicate when your trade is Green because of these abilities (Say... Having the AI screen say something to the effect of "Well.. I normally wouldn't do this..."). That will make it easier to see just how much benefit you are getting from them. As for ways to make them less similar... well... I don't have any at the moment.
Super Trader - This ability is mostly fine, but I don't think it really fits the Korx, given they are an evil race and they might get their only unique benefit nullified by a UP Issue.
Keep the Super Trader ability in the game (for the use of custom races/opponents), but make a new Super Ability for the Korx as detailed below:
SUPER SMUGGLER -
This race is adept at smuggling trade goods. They start out with the Trade Tech and their number of trade routes is never reduced. In addition, their Trade Routes are immune to attacks and are not disbanded during war (ie: although they can't establish new trade routes with races they are at war with, they get to keep the ones they currently have with that race).
And as a last note, the Super Trader ability should give a bonus to Diplomacy when making trades where one side of the deal is only money (and maybe Economic Treaties).
Super Breeder - The current bonus is fine but to make it better compare to the other abilities here have the planet they start with in the beginning of the game already have the max population supported by the Civilization Capital and half the morale penalties due to high populations on worlds they
colonize (but not get through invasions or culture flipping). A race that breeds super fast probably should also be able to better deal with large numbers of themselves.
Super Adaptable - I suppose this can provide a strong bonus in a game with a lot of Special Worlds, but I propose this revision to it to bring it up to speed with the better Supers:
This race can colonize ANY world in the beginning of the game. However, these worlds only produce 25% as much production as normal and population growth on special worlds is hindered by its production value (thus, the super adaptable race on a planet they can colonize at 50% has its population growth at 50% slower on that world). The cost of research Xeno Biology and its later techs should also be reduced by some amount for the race.
With these changes, a Super Adaptable race would be to capture a lot of worlds if they wanted to, but it would be hard for them to build up these worlds at first and they also wouldn't be able to get the population base needed to be able to support these worlds without taking a huge hit to their economy.
Super Spy - Rather than making their worlds immune to spies and giving them a free agent at the start of the game, I would give them the ability to automatically nullify one random agent on one of their worlds at no cost and without the use of an agent at the
END of each of their turns. Also, no race can get a higher than Low Espionage Level with them and the Super Spy race always has at least a Low Espionage level with every race they have had contact with.
In this way, you can still spy on a Super Spy, but it will be
very costly to maintain (since you are might to have to place a new agent each turn). Not allowing any race to have a higher than Low Espionage level maintains the "Hey, I'm a MYSTERIOUS and SECRETIVE race! OoOoO!" feel of the Super Spy ability.
Super Isolationist This is a very good racial ability as is. The only thing I suggest is a diplomacy/influence/trade penalty, as others have stated above. Maybe also a Loyalty bonus, if the penalties are high enough.
Super Hive This is also a very good racial ability as is. The Unlimited range is a nice ability, but it can hinder you as much as it helps (since by the time you might get a ship to the other side of the galaxy, you'll likely have much more advanced ships in your arsenal, so its only really good for non-military purposes. Its the build factories in one week that could be a problem. I might suggest taking on a Speed penalty to the ability to help balance it. Of course, maybe I've just been playing too much Sword of the Stars lately...

A second option would be to make
literally only Factories (and Basic Factories) be built in a single week. The higher tech Factories would take the normal time. This is probably the better option.
Super Warrior Great ability as is. But can I make a suggestion and have it NOT apply to Cargo Hulls (or preferably any hull marked in the xml files with a special property)? If possible, I might also suggest they only get the first strike in combats they initiated.
Super Dominator I really hope you keep the ability for them to better be able to get bribes/extortions. If you do, I would definitely also suggest making sure it is clearly apparent when it is your ability and not normal circumstances that is letting you get the trade.
The gaining of ships when you go to war does need two tweaks:
1. They gain the bonus ships only once every year they declare war on a particular race or they should disappear when you are no longer at war with that race.
2. The maintenance cost of the ships should probably be reduced/eliminated so as to make sure it is not going to be a hindrance rather than a bonus (especially with the AI).
Super Organizer - Great, flavorful ability. Two suggestions, however:
1. Give them a diplomacy bonus when they are making trades in which one side of the deal is only Influence points, Treaties, or Alliances. Maybe lax the requirements for making Treaties/Alliances.
2. Make it completely clear when it is this ability that is having a particular race declare war (or when you are getting a trade as above) on your enemies (as with the other abilities that deal with the diplomacy engine).
Super Annihilator - Another great, flavorful ability. I agree that this ability isn't as powerful as it seems to be. I really don't have any other suggestions with it, though.
General Super Ability Issues:
1. Races that start out with bonus techs because of their Super Ability should be incredibly reluctant to trade them away, especially during the better part of the first decade of the game or so.
2. There should be an easy way to see what Super Ability a race has in game.
3. There should be a way to completely disable all Super Abilities.
4. Not having a super ability should give that race more ability points to spend, unless super abilities are disabled entirely.
5. I'd like to see more, unused Super Abilities be added that can be used with custom races/opponents.
6. Influence, Diplomacy, and Trade penalties that Super Abilities might get shouldn't apply when dealing with other races that have the same Super Ability.
7. Along with the recent change to make innate abilities stack with the Ability Point choices you make (which I really, really hope stays), the Super Abilities add the single largest layer of strategy/flavor out of any of the additions so far, imho.
Well... sorry for the long post, but I really hope that people read and comment on it. Good job so far with the super abilities!