Question on the properties of red black trees
The left subtree cannot be a chain of $n$ black nodes, since it breaks the red-black tree properties.

In the worst case scenario, the left subtree is a minimal black binary tree of  height $\log n$, while the right subtree is a full maximal binary tree of height $2\log n$. 

The black height of the right subtree must be $\log n$ as well, therefore its maximal total height (including red nodes) is $2\log n$. Since it is a maximal binary tree, it has
$ 2^{2\log n}  = 2^{\log n^2} = n^2 $ nodes.