While I can't answer all of the questions asked, I can add some additional information. I'm drawing my sources from Wookieepedia and from what I remember of the last few books.
Firstly, your initial premise that the organic creatures used as weapons/tools were created by accident by some creative Yuuzhan Vong is incorrect. Towards the end of New Jedi Order (don't have my books on me, so I can't remember which ones), it is established that when the Vong first lived on Yuuzhan-tar (the living world that Zonama Sekot is a child/seed of) they were attacked by a machine-using race. In response, Yuuzhan-tar made its creatures rapidly evolve into weapons that the early Vong could use to defend themselves. They succeeded in this venture, but turned to valuing combat prowess above all others, at which point their 'gods' abandoned them.
"The ancient texts are unclear. It appears we were invaded by a race that was more technological than animate. We called on the gods for protection, and they came to our aid, providing us with the knowledge we needed to convert our living resources to weapons. We defeated the threat, and, empowered by our victory, we gradually became conquerors of other species and civilizations."
Harrar - The Unifying Force
So it was Yuuzhan-tar that was responsible for initially creating these creatures (or their predecessors) rather than the Yuuzhan Vong themselves. However, the Yuuzhan Vong do have access to some creatures that have a limited ability to sense their user's emotions.
- The amphistaff can harden any part of its body at its owner's will.
- The coralskipper can manoeuvre and fight in space by sensing the will of the individual wearing the cognition hood.
- The yammosk as detailed below:
A yammosk was an incredibly powerful organism that served as a type of biological Battle analysis computer. It did this through empathic abilities that bordered on telepathy and the creature was capable of communicating by the manipulation of gravitational waves.
There may be others. The shapers may have analysed these connections when creating new lifeforms for their race to use.
In regards to villips specifically, it seems they were present on Yuuzhan-tar from the start, and their telepathic ability was meant to warn the rest of the organism about predators.
Two to five berries would bud from the stalks, feeding symbiotically and developing telepathic communication channels originally meant to scan for predators on the villip plant's home planet. Soon the berries grew to about the size of a Yuuzhan Vong's head, and Shapers would pluck the matured villips from their stalks
The communicatory relays between the 'sister' villips, however, would not be lost. Telepathic networks would persist between the stalkmates, allowing them to communicate instantaneously across infinite distances. Yuuzhan Vong took advantage of this natural predilection and utilized villips as the ultimate form of long-range correspondence.
Finally, we get to the subject of Onimi. I believe that in the climax, when Jacen realised that Onimi was Force-sensitive, he also realised that Onimi had achieved this through sheer dumb luck.
After adding yammosk tissue to his brain (which was most likely the action that restored his connection to the Force, given the yammosk's natural telepathy), Onimi was marked as a Shamed One,
Judging from this, it is very likely Onimi was the only member of the Yuuzhan Vong race to have achieved this. And due to his 'public' standing as a Shamed One, he was not really in a position to share this knowledge with anyone else. It might not be too far fetched to assume that not even Onimi realised what he had done at the time, since he stuck to subtly manipulating Shimraa. Thus, the only chance he got to fully test his capabilities and go 'all out' was against Jacen.
