As a small quibble, there is no such distinction between "laws" and "theories". In common language a theory may imply less certainty than a law, but in science this is not the case.
[Yes i am aware that atoms don't necessarily conflict with waves]
Law: A simple relation of limited scope intended to describe a single phenomenon, for example Ohm's Law.
Theory: A description or narrative of how and why, which may include laws, data, observations, etc.
There is according to the academic circles I participated in, although it wouldn't surprise me if most physicists you meet wouldn't know that.
I don't think the principle has anything to do with the difficulty or hardness of falsification. If a theory excludes something from occurring in reality, it is falsifiable, if it does not, then it is not falsifiable.
So think about it like this, if a theory is "compatible" with everything that happens, it really does not make any predictions, as regardless of what happens, the theory holds. What the point of such a theory is is unclear.
General relativity precludes many things from happening, and many tests have been performed that would have detected things that general relativity precludes from occurring: https://en.wikipedia.org/wiki/Tests_of_general_relativity
Yes, I agree, but like I said it's much harder to find what these are and create experiments to show them. I'm also saying the theory part is more than the math formula, it's the explanation.