A collection of Isomorphic Groups 
So the answer is

Questions
1) How exactly is $<\pi>$ isomorphic to the other integer groups? I mean $\pi$ itself isn't even an integer.
2)What is exactly is the key saying for the single element sets? Are they trying to say they are isomorphic to themselves?
3) How exactly is $\{\mathbb{Z_6}, G \}$ and $\{ \mathbb{Z_2}, S_2\}$ isomorphic?

1) Notice that $\langle \pi \rangle=\{\pi^n \mid n \in \mathbb Z\}$ and we also have $\pi^n\pi^m=\pi^{n+m}$ what group does this remind you of?
2) The single element sets are not isomorphic to any of the other groups. As an aside it's not particularly meaningful to say a group is isomorphic to itself. You generally speak of two groups that are distinct in some meaningful way as being isomorphic. 
