She was a very basic human with psionic abilities. Only chosen because Humans are still in their infancy in terms of psionic abilities. Her psionic abilities are subpar when compared to any other creature in Starcraft, Nothing which changed when she was infested.
Not so much. She was one of the most elite Ghosts, who themselves represent the pinnacle of human physical and psychological achievement. That was prior to infestation. During infestation, her subliminal consciousness was so disturbed by her metamorphosis that she sent out a psionic call across the entire Koprulu sector, drawing Raynor and his forces to the planet on which her chrysalis was located.
The reason the Overmind chose her is because during the raid on Tarsonis she was a curious human that emanated strong psionic potential, which to it meant both something interesting and a potential weapon against the Protoss...it saw in her mental radiation the potential for the Swarm's greatest creation.
Oh, and as for "subpar compared to any other creature in Starcraft..." After breaking into the Amerigo and recovering the data files on her, she unlocks her ability to actually create psionic storms the likes of which only the High Templar (considered the most psionically powerful of the Protoss upper tier) are able to duplicate. Not to mention, in the Overmind's absence she calmed and dominated the entire Zerg Swarm. Don't take her psionic abilities too lightly.
The Humans were tools to be used to attack at the protoss, nothing more. Kerrigan was one of the humans whose pisonic abilities made her stand out amongst a race who was still prematurely developing it. Similarly the Overmind was incredibly powerful, and so often people don't really begin to realize how insane that creature was. There was no way the overmind could have taken a human and made her more powerful than itself.
Humans were food and host material, not tools. KERRIGAN was an experiment the Overmind came up with when it discovered a strangely potent psionic field coming from a
human, a race previously thought to be nothing more than organized animals. The Overmind didn't intend to create something more powerful than itself...how she turned out wasn't deliberate, only a result of the genetic reworking that the Zerg DNA performed on her. Zerg mutation isn't intelligently designed, it's hyper-evolution. The Overmind inducted Kerrigan into the Swarm to see what a "perfect human specimen" could yield. Its own superiority complex kept it from seeing what it had done and realizing that it indeed HAD made "a monster."
And secondly the New overmind was destroyed because Kerrigan of specificly. Kerrigan used the fears of her enemies of a greater threat to dismantle the UED and strike at the Overmind. She was the reason the overmind was destroyed. Remember she couldn't control the Cerebrates or the other zerg broods under their control BUT if the overmind had reached maturity, the Overmind would have enslaved her again, thus is the power of the Overmind.
Kerrigan destroyed the young Overmind because it would have disrupted her control over the Zerg she commanded. Of course she can't control Cerebrates...technically neither could the Overmind. The Overmind was vastly more intelligent than the cerebrates and it gave them orders, but Cerebrates were sentient as well with their own wills and personalities. They merely followed their orders because it was what they were genetically created to do...there was never a question over whether or not they should, they were being directed by the Overmind.
I have my doubts that the Overmind ever truly had enslaved her. She fed some of her "allies" that line to get them to join her cause, but she always spoke with sentience and a true sense of self. I believe she was on the same level as the Cerebrates themselves.
Oh, and let's not forget one psionic achievement she has over the Overmind. Who's the one who completely took over the mind of Raszagal, a very old and powerful Dark Templar matriarch? That would be Kerrigan. The Overmind never managed to actually manipulate the minds of a race that's pure core is psionic ability and power...Kerrigan did.
Don't underestimate her power. She took over the entire Koprulu sector under her own power. When the mad fury of the swarm wouldn't get the job done, she manipulated her enemies to become her allies and got it done that way. The chick is seriously scary, and underestimating her is what got a lot of folks killed...namely Fenix, and Duke.