>Is the cooked-for-you food free? It's broadly true in the US as far as I know for on-campus university housing. (Off-campus housing and fraternities/sororities are often different.)

Anything but free. Meal plan requirements vary.

Where I lived undergrad, we had a kitchen for a suite of rooms although I ate out a fair bit. (Many dorms did not have cooking facilities though.) Both places I went for grad school (which were actually both Ivy League) had no cooking facilities of any type.