What is the opinion of Islamic law regarding the solar storm rumors that Western scientists are talking about, and how can Muslim youth be protected from being affected by them?

There is nothing in the Sharia that proves or refutes this matter. If its proponents rely on empirical theories, then their words are not considered a claim to the unseen. Rather, it is an expectation that may or may not occur, and it cannot be definitively affirmed because it is nothing more than conjecture and estimation.