Carl Schmitt would agree, or maybe Helmut Schmidt, too, when he was Mayor of Hamburg in 1962: "We didn't refer to the Constitution much, in those days"

I would classify occupying buildings and shared areas as a technically illegal but often legitimate form of protest. Many spaces, which are in principle owned or controlled by a specific entity, are functionally indistinguishable from public spaces. Protesting in them should be allowed under the same conditions as in public spaces. Which should mean that permits are not required, but the protesters are expected to cooperate with the authorities. And that the authorities should strive to find a good balance between the freedom of speech of the protesters and the disruption caused to bystanders.

Besides, students occupying university buildings for random reasons is just business as usual. It's something that should be expected when you have institutions with a large number of young ambitious people with minimal supervision.

That doesn't fit the definition of protest, that's harassment. The former is protected by 1st amendment, the latter is not. It is important to use the right words.

That just means that Columbia doesn’t value research except as a way to get money from the government.