Sure, the first is only true for water at room temperature. It is particularity dangerous idea to mix up mass and volume in physics.

I mean, it's middle school science, so being true at room temperature seems totally reasonable. Anyone for whom it is a particularly "dangerous" idea will cover the irregularities in a higher level class...

I mean, to some degree, all content areas are simplified at different levels. And the measurement is technically correct. The point of such measurements at the MS level is likely to understand conversions in general, frankly.

The second is an impossible figure - I already explained in another post. If you calculate the area through Heron's formula, or use Pythagorean theorem on the small triangle, you will see that.

The triangle is wrong, but what is it being used for? It's not like teachers can select the texts. If it can be used for the problem, even as an impossible triangle, in order to teach the standard, I think you're being a bit excessive. The teacher responded with how students should solve the problem for this standard because that is her primary focus.