when teresa and the concept of partial awakening were introduced, i was inclined to believe that she hadn't partially awakened. with regard to this, one of the main problems i came across was the fact that clare wasn't able to access any of teresa's incredible strength until after she partially awakened. this means the power was latent. while clare was only half of teresa, i'm inclined to believe that the same limit would be in place for teresa. teresa's partial awakening would have been one of the organization's experiments (obviously, the best time to do something like that would be right after turning the human into a hybrid in order to limit the negative side-effects of uncontrollable attempts). they had to go in some new directions after what happened with luciela. one of those directions was the twins, strengthening the yoki bond between the awakened and the controller. another possible direction would have been to take the controller out of the equation by strengthening the will of the test subject. they'd pretty much be imitating the process but would find a way to bring her back without a controller (individual will has proven to be strong enough to reverse an awakening and teresa had a pretty strong will). of course, she was suspicious of the organization and tried to limit their knowledge of her progression. after teresa's little rebellion, they decided the shelve the experiment because it was too dangerous.
also, every claymore eventually has to talk to their handler in order to get new equipment and orders.
Sorry but all this makes no sense to me, first if teresa as actually the first half-awaken experiment she would have being a huge sucess leading to many others like her to come, and that didnt happen, makes no sense to drop a project because 1 experiment rebellion all they would have to do was create a more obdiant claymore (luciella/rafaela were also powerfull and were even a bigger failiture and the orga didnt gave up on her project and at the time the orga was almost destroied 1 experiment rebellion is nothing near that).Half-awakening is no explanation to why she was so strong, priscilla was also incredible strong and she wasent even used to her amoung of power.Teresa was strong the organization knew that of course (otherwise she wouldnt be n1) whoever they didnt knew with accurance how strong she was (as far as we know she never used more than 10% of her youki) so they couldnt be sure if she would be able to fight an abysmal one and of course they wouldnt risky losing a warrior like her if they wasent sure she would win, besides it was the organization policy to ignore the abysmal ones if im not mistaken all awaken ones were ignored and had the same treatment that normal youmas (someone requests to kill the "thing" they send someone to kill it and colect the money).To finish it of Teresa didnt like the org. but she still followed her others without complaning i dont see how meeting with the abysmal ones would change anything, she already had the streght to flee if she really wanted to, besides until isley met priscilla and assembled his army all the abysmal ones were quite inactive as riful said it herself (she started looking for claymores when she heard of isley army) so the chances of their meeting was pretty low.
Edit: Btw claire streght didnt came from her half awakening, it was mainly due to she training since long time to read yoki (miria mentioned that when they fought the first awakened male, that she learned to be a good yoki reader in order to fight awaken creates), and from she getting ilena(is that her name?) arms and learning her quick sword skill and of course the experience she got from each fight.
But, half-awakening (going beyond the safe yoki usage limit but reverting back to human) DO boosts characteristics.
And, we can't tell for sure if Organization did experiment on that, but deemed it not powerful enough.
yes, miria's handler is considered by lots of people as a likely candidate. He was watching miria, deneve, helen and clare take on the male awakened. I think that teresa didn't go after AO just because the orgs policy was not to. As long as they hid, there was no problem.
Teresa might have partially awakened, but I don't believe she did and if she did I'm pretty positive it wasn't the result of experiment because she was a "problem child" the Org. wouldn't trust her with the responsibility of being partially awakened. And if the Org. was scared of failing experiments there wouldn't even be a second generation of warriors (the male ones cuz they were first) because Isley's generation was the very first generation of Claymores ever and he, Rigardo (the number 2) and Dauf (number 3) (and I think in the anime the number 4 was there too but not sure) awakened in presumably about the same time frame, which would have caused GREAT devestation to the Organization. And Riful was the in the first gen. of female warrioirs and was the number 1 of that gen., so the first female number 1.