Identifying Errors in Proofs

A student attempts to prove: If $n^2$ is even, then $n$ is even.

Argument:

1. If $n$ is even, then $n^2$ is even. Therefore, when $n^2$ is even, $n$ must be even.
2. Suppose $n^2=2k$ for some integer $k$. Dividing by $n$ gives $n=\dfrac{2k}{n}$, so $n$ is even because the right-hand side has a factor of $2$.
3. By definition, an integer is even if it is a multiple of $4$. Hence $n$ is even.

Consider the following claims about the argument above:
I. Line 1 confuses a necessary condition with a sufficient one: from "if $n$ is even then $n^2$ is even" it infers $n$ is even when $n^2$ is even (affirming the consequent).
II. Line 2 misuses algebra and the definition of even: from $n=\dfrac{2k}{n}$ it concludes $n$ is even by "seeing a factor 2", but $k/n$ need not be an integer.
III. Line 3 misstates the definition of even: being a multiple of $4$ is sufficient for being even but is not the definition.

Which of I–III correctly identify errors concerning necessary/sufficient conditions or related definitions?