why was the school inside the military compound

It wasn't.

why did the US take the risk of striking it

Due to appalling incompetence which made them think it was part of the military compound. This should be investigated as a war crime, it's an unacceptable mistake.

This is extremely tragic, and very worrying that the US cannot seem to admit to its mistake officially. It's also obvious that the Islamic regime is taking this excellent chance to use in their propaganda against the US and Israel, because why shouldn't they? It also undermines trust and hope that some Iranians have in that this may lead to a regime change.

That said, there is one thing true in what you stated, and that is that there may be some manipulation of the true death toll and other reporting of it, because the only source of it is the Islamic regime and they have an interest in making it appear as barbaric as possible. And as you said, neither side can be trusted, you can expect propaganda from both sides.