The way I read that it says everything that is not part of $A$,$B$ and $C$. So the answer is $U$ from my diagram?

The way I read that it says everything that is not part of $A$,$B$ and $C$. So the answer is $U$ from my diagram?

Recall the De Morgan's law for sets. $$(\sim A) \cap (\sim B) \cap (\sim C) = \sim (A \cup B \cup C)$$ Now you should be able to conclude what you want.
Yes! You can try shading each of $\sim\! A$, $\sim\! B$, and $\sim\! C$ in three different ways, and see where all three shadings occur.
Using D'Morgan's law, $\sim A\cap \sim B \cap\sim C=\sim(A\cup B\cup C)$ which is the region $U$. $\sim $ behaves like a negative sign and converts $\cap\to \cup$ and $\cup \to \cap$ and sets to their complements.