After learning Shetty's true intent and that Cate is a telepath capable of reading minds, it makes sense that Shetty would give her pills meant to suppress her telepathy: because it would prevent Cate from poking inside her head and uncovering her plans to engage in Supe genocide.
The revelation of Shetty's true intent also would explain why she blackmailed Tek Knight into dropping his investigation when he contemplated scapegoating her for Golden Boy's death. She wanted him gone before he could poke around too much and uncover her plans, which she doesn't want the higher ups at Vought to be aware of.
The first episode establishes that the windows in the dorms at Godolkin U don't open; Emma claims it was because students capable of flight would jump out of them recklessly. But during the second episode, while she's on the phone with Ashley, Shetty says that that she had "hardly any suicides" after the truth of Compound V came out; this raises the question of whether the windows were sealed before or after the suicides occurred.
When Cate and Sam free the prisoners from the Woods, Cate asks one of the prisoners when he last ever set foot outside. The prisoner in question asks her if Gangnam Style is still a thing. This would suggest that he's been a prisoner of the Woods for at least a decade. And given how he looks to be in his late 20s / early 30s, he might very well have been a student at God U when he was sent here.
