I keep getting these right because I'm going so slow. Are we supposed to be taking notes as we answer these questions or no? I feel like I've heard conflicting info about that, but I find it impossible not to.

In my understanding the second one is really similar to your answer, and "It is not the case" functions the same as "not"? But maybe someone else disagrees?

For the takeaway questions, did anyone answer the last one? I didn't realize you could "counter" a correlation. It makes sense to me that you could "counter" a causal relationship, but not a correlation, given that a correlation is a fact?? Maybe I'm misinterpreting the question/the terms?