This is correct.
This is sort of correct, but just to be clear: “the equation” here refers to QFT as a whole, not necessarily the statement about no particles in particular. I don’t know if anyone has directly experimentally verified specifically the statement that there are no particles when there is no oscillation. By itself, this statement doesn’t mean much to an experimental physicist. To actually test QFT, you need to convert theoretical, mathematical statements like these into statements about quantities that are accessible in the lab. This is we test QFT by say, measuring the magnetism (or g-factor) of the electron (see explanation here). Because QFT turns out to be extraordinarily correct in most of these tests, we think that it is a robust theory and we can believe its claims more generally without having to test every single equation directly (if that is even a coherent notion to talk about).