The Tengu Shredder targets her because it feels that by taking on the mantle of the Shredder, she defiles the name and such. The Turtles come to her aide because the four of them, Splinter and the Ancient One all had visions indicating to them that Karai had her own part to play in stopping the Tengu Shredder and had to be kept alive.
The Tengu Shredder injures her, but Chaplain and the Turtles rescue her and April bandages her wounds. She recovers, and they all learn that all those who have taken the mantle of the Shredder, including the Utrom imposter and Karai, share a telepathic energy link with the Tengu Shredder, giving them the ability to sap the Tengu of his demonic power through the link. She declares a "temporary" truce with the Turtles, and plays that very role during the final battle, sapping the Tengu Shredder's immense strength, weakening him enough for the Turtles to defeat him once and for all.
Chaplin has an obvious affection for Karai, which seems unrequited, but at the very end of the finale, Karai takes Chaplain's hand and walks off into the sunrise, stating that it's a new day and wondering what it will bring.
Whether Karai has softened her stance on the Turtles is not implicitly stated, however it seems logical enough - they did save her life and her empire from a demon bent on world domination - and in the Fast Forward episode "The Journal", when Leonardo returns to the Ninja Tribunal's monastery to continue his training, he encounters Karai there as well, who actually says it's "good to see him." Despite that, Leo still doesn't trust her completely. Keep in mind, the journal the Turtles read in that episode was actually a fabrication created by Cody, and therefore none of the events described in its pages actually happen (happened?). With that said, I would think that in order to make the journal believable at first read, Cody would have had to create it with the historical truth in mind, such as having Karai drop her grudge against the Turtles, as it is what Leonardo would expect to find in a journal of the events following the Turtles' return to the present, based on the resolution of the Tengu Shredder conflict.