super diplo really a/e-ffects many things. The main one is that you can interact with the other races every few WEEKS as opposed to every few MONTHS. But it also gets you cheaper prices/better trades in the diplomacy window, allowing you to barter for basically anything. Ships, treaties, start/end wars, etc. Not sure that the super diplo has anything directly connected to influence exerted on other planets, other than the leaders maybe liking you more.
I'm pretty sure they get an Influence bonus along side the above bonuses. I've also rarely ever been above the Terrans in Diplomacy if they roughly the same number of Diplo techs researched as I do, even with Diplo Translators and the one Galactic Achievement so the bonus is probably pretty significant.
And it's 'affects'. Affect is the verb, effect's the noun. You don't wanna
know how many times I had to hear that last semester... *sighs

Hive = cheaper factories, better sensors. But only YOUR factories. EG. If you conquer a planet and pay to upgrade one of their factories you dont get the discount.
Faster built factories, you mean. It might do this by reducing the overall cost, I dunno (originally, they could build any factory in one turn!). They also get better range, not sensors (originally, they had INFINITE range!).
Manipulator = starting wars is easier
And a general bonus to Diplomacy too, but nothing to the extent the Terran get.
Korath (whatever the name is) = spore module. You can add this module to a ship and it allows you to conquer the planet without a fight and it becomes toxic. You have to clear out and fleet in orbit first though.
Super Annihilator. They also get Toxic World Colonization for free, which REALLY cheapens Super Adaptable, IMNSHO.
Drengin get these little crappy corvette ships when they go to war. The number of ships I think is dependant on the difference in military strength of the 2 factions at war.
They also get a bonus to extorting money from weaker civilizations. Doesn't affect the player, though.
Altarians can request assistance from like minded ethically races to join in a war only when someone declares war on them. Not when you declare war on someone though.
Note that the Comp Civs with the same Alignment as them will ALWAYS declare war on the Civ that declares War on the Altarians. A little pop up window will come up if the player is the same alignment as the Altarians, but you don't have to go to war.
It's a pretty nice ability in all honesty, but the AI doesn't seem to take the ability into consideration when deciding to declare war on the Altarians... if it did, it would probably be a lot better and very useful for those trying for one of the more peaceful Victories.
Trader gets extra trade routes and all the techs already researched.
They get DOUBLE the income from Trade Routes, not extra ones and
any tech in the game that has a +Trade bonus (including any you might mod in), unless it is an alignment-specific tech (or not in their Tech Tree, in the case of TA Beta)
Spy gets counter espionage already researched, a discount on making spies, and you start with 1 spy.
It's not a discount, they just get to spend extra money each week on Espionage than normal *twirls finger in excitement... (originally, they were outright immune to spies... then came the Counter Espionage tech and took it all away from them (
)
And to the op... if you are looking for exact numbers, you are unlikely to find them. There doesn't seem to be a lot of... what does the Kingdom of Loathing community call 'em... "spades" in the GalCiv community. Ie: people who get a thrill out of "digging" around in the game, testing things to figure out exact numbers, exact probabilities, and the exact mechanics in the game...