The contractors don't directly teach the model. They create datasets. Mostly they create tasks within an environment that the current generation of models wouldn't be able to do, they then write maybe a solution, a set of rules for evaluating the response, and whatever is needed for the RL. These tasks form a dataset. You can see examples of a task in the Mimo dataset that was open-sourced recently. The dataset would then be used by engineers for post-training of whatever model. Some of the model iterations that are released every month tend to be just a further post-training of the same base model that was pre-trained months ago. OAI recently has been doing a lot more pre-training, but for a long time they had the same pre-trained base model. This is why you see so many releases done so fast by the labs, they just need to post-train the same base model on whatever task they think would be better suited, I would speculate based on what users want and what the benchmarks test for.

Regarding your second question, I think if they want to further post-train a model using new data, they wouldn't feel the need to re-train it again on the data that it has already being trained on. But you never know. If the model is a completely new pre-trained base model, then they could either train the model using all the data and/or use a previous model to teach it. There is definitely a bunch of tricks they do to evaluate the models and check the performance or whatever their recipe is. It's really up to what the engineers would prefer. But you get the core idea, the models are not suddenly coming up with how to use the Blender on their own, they are explicitly being trained on a dataset curated by a professional that teaches the model how to use Blender. Surely there is another aspect that if the model gets better at coding, then it also helps it become better at Blender, and you have that transfer learning. However, there is no emergence or a deity popping up. But you get people who were evaluating theses models on blender use and suddenly seeing the model ace their tasks and they think they are dealing with a super-intelligence. They then undergo an AI psychosis once they try and extrapolate the (super)-exponential improvement in that one task over the next few months and across all other domains.

Regarding your third question, I already answered at it. But, when it comes to training, they definitely freeze the weights after each run just in case an issue arises and they need to address it (a GPU not working or the loss value blowing up).