If I were going to balance these abilities with penalties, this is what I'd do. This is based primarily on the "feel" of the super ability; I'm only considering balance as a secondary consideration.
Super Diplomat. Civilization is able to secure much better deals through negotiation that other civilizations.
maybe this should be balanced by ding (negative point) in the relation screen. the ability isn't "super likable". to me it means humans can wheel and deal at the negotiation table, other races perhaps realizing they've been ripped off afterwards. so while human can negotiate good deals, other races will be more likely to go to war when they get fed up with it.
Super Dominator. When they go to war, they receive a group of Corvette class ships. The number they receive is based on their military power.
because their people are general warmongers, they receive a morale penatly for a year or so after signing a peace treaty. this'll also keep players from constantly declaring war and signing treaties.
Super Organizer. When they are attacked, all races of the same ethical alignment will come to their aid.
the name makes me think of bureaucrats. perhaps a production penalty. side note: if the altarians are "super organizers" why is their logistics value so low?
Super Warrior. When in battles, they get the first strike ability. That is, their ships attack first and if their opponent survives only then do they return fire.
makes them sound honorable but impulsive. perhaps they should receive the logistics penalty.
Super Breeder. If their approval is 100% their population increases at 4X the normal rate.
automatic morale penalty when planet's pop max is reached. law population control anger them.
Super Isolationist. Can colonize barren worlds and no foreign ship can travel more than 3 spaces per turn in their area of influence.
influence and/or trade penalties, as suggested.
Super Trader. Gets all the trade techs at start of game and gets 2X from trade.
i like the idea mentioned about about changing this to "super smugglers." they make 2X because they're dealing in black market products. as smugglers, you could also add the bonus that their trade lines are invisible. however, the civs they trade with don't get any money (since the trade is illegal), and thus the korx don't get any boost in their diplomatic relations -- or they're charged negatively for smuggling.
Super Manipulator. Is very good at getting other races to go to war with each other.
i agree that this is very similar to the terran ability in some respects, and it also kind of reminds me of the altarian one. perhaps if they were able to influence another player's opinion of a race it'd be more interesting, or perhaps change it entirely to focus more on the united planets or something along those lines.
either way, i think a good counter balance is that the computer oponents are more likely to declare war on the drath the more they use this ability, the same way they'll gang up on almost anyone who's getting too powerful.
Super Hive. Unlimited range and all factories are built in 1 week.
reduced research ability (hive mind lacks individual creativity), reduced trade (the hive is self-sufficient), reduced diplomacy (the hive isn't used to communicating with others).
Super Adapter. Starts out with aquatic and toxic world technologies.
i'd like to see this one implemented differently. rather than having the techs, the iconians simply have the ability to colonize these worlds. they'll only have access of half the tiles, and all of their production, population, etc. will receive an even greater penalty until they've researched the technology. not sure how i'd balance this ability... maybe since they're adaptable they lack an environment perfectly suited for them, and ALL their colonies suffer some penalty until they research extreme colonization.
Super Annihilator. Can build spore ship which when used on a defenseless colony will eliminate all population and turn it into a toxic world of the same class.
instantly and permanently at war with any race they encounter? that seems a bit harsh. perhaps a better balance would be that they cannot form aliances or even trade.
Super Spy. Gets an agent to start with and worlds are immune from agents.
nice. i'm gonna go with my first instinct: they're spies cost considerably more, since they're so well trained. well, the way the ability is now, it's not that their spies are well trained, but that their civilians are trained in counter-espionage. so maybe give them a significant economic penalty that represents that cost of training their whole population, but allow them to train spies at reduced cost (since everyone already has some training).
...not that you don't have enough work on your hands. some ideas for possible extra abilities (which i think would be a good thing in theory, perhaps too much work in the long run; still, it would be nice to have 1 or 2 for custom races).
super commercialists: a bonus to influence and double or triple income from tourism. balance with trade offers
super spacefarers: starbases have larger areas of effect, planets covered by a SB area of effect automatically receieve a morale bonus.
super survivors: ships destroyed in battle have a some% chance of "surviving" after the battle with 1HP.
super minds: rather than a basic research bonus, the race with this ability can actually skip iterations of certain technologies.
dirty politicians: only half as likely for major party to lose elections/higher window of disapproval for it to happen, receive twice as many UP votes, and kickbacks from halliburton.