Confusion over the complexity of parameter passing in merge sort
The $N$ is incurred once for every recursive call, since this is the cost of passing a parameter. Since there are two recursive calls, it's $2N$. As for the $4N$, this seems like a mistake. Don't expect solutions you find on the internet to be correct. Finally, $N$ is not a subset of $n$. It is the size of the original array. A less confusing way to write the conclusion would be $\Theta(nN) = \Theta(N^2)$. Note that it is always the case that $n \leq N$ (and not the other way around).