There is no such thing as "pure science". All scientific theories require so framework by which to understand them. Saying the framework is math isnt lesser.

Sure but you can rule certain explanations through experiments designed to spot the differences this is well known in science. And scientists design experiments all the time to do this.

Occums razor isnt a rule you must follow. In science the best theory is the one that makes the most testable hypothesises.

No one in science thinks the models are right they simply think they are most correct ones we have. Which is true if there's a flaw science will inevitably course correct, and that's already been happening with multiple physics theories losing popularity and some other ideas coming back. The issue is people assuming one idea is right and more worthy of research without any understanding of them.

The simpler answer may seem correct but the universe is under no obligation to be simple, or even be intuitive to us at all.

They can explain it, they can explain it mathematically and theoretically they've designed experiments based on models and have some observational evidence your just to stupid to understand the science