1) We aren't sure what happened to Tychus yet. We hear a gunshot, then the scene fades out, basically. But we don't know if or in what part of the body Jim shot him. For all we know, he shot the suit's antenna off in some action-hero fashion which shut down all the kill switch hardware and caused the suit to unlock while simultaneously giving Mengsk the impression that he was killed and failed his mission.

2) While Kerrigan is now significantly less Zerged, don't forget that she was among the most powerful telepaths in the human race. I wouldn't be surprised if she still has the ability to control the swarm. Some scenes depict her treating them like children or pets and showing them affection, which is even returned to a mild degree (I refer to the petting of Hydralisks in cinematics and comforting the one that was dying).

3) It's clear that Dr. Narud and the Moebius foundation were not exactly what they were portrayed to be. The obvious connection between the names Narud and Duran is only the chunkiest evidence. We also have questions from this thread, such as how did they know about the Xel'naga artifacts at all, let alone what those artifacts might do to the Zerg or Kerrigan? How might this figure in to the Xel'naga's master plan? The future that Zeratul saw was only one slice of the space-time continuum, one dependent upon Raynor's Raiders killing Kerrigan. It's entirely possible that the force behind the scenes (The Fallen One?) possesses prescience as well, and has worked the latest developments into its plans as well.