Yes I would say most of physics we currently can make predictions with are just effective models that are only applicable at some certain scale. Certainly there may be some underlying ideas that get shared around but doing calculations and making predictions is effective.
Yes, they are in absolute terms. To prove that they are exact we would need to have a complete understanding of the universe, which we do not have.
In practical terms, some of them are in the sense that it is impossible to measure their inaccuracy with common equipment and our primitive human senses. In the end, their purpose is to make predictions and help us make sense of what’s around us, they do not need to be exact.
The ones you learn in high school are, but general and special relativity are accurate to trillionths of a percent (their approximations at low speed and without time dilation are the high school equations).
We don’t know if they break down, because we have no means of measuring them more accurately on earth with all the statistical fluctuations happening.
I think the point is that with conventional equations we can make increasingly better approximations by just using pen and paper, while with these ML methods, you need to train your system ab initio if you want to improve your approximations.