2. I would say she figures out that it might based on "magic numbers" or numbers with significance. Maybe she thinks there are 4? Four elements, four houses, solid sort of thought. And the thinking behind it could ultimately lead more closer to the truth.
3. Zombies, Clare, everyone is going to become zombies.
4. I'm all for you to run with this. Voldemort's body is definitely gone. She can say that with certainty. Parts of his soul are still elsewhere. With that roll, I would even let her think that part of his soul might be in another person or animal.