What is the minimum and maximum number of eigenvectors?

Correct, an $n\times n$ matrix which is diagonalizable must have a set of $n$ linearly independent eigenvectors -- the columns of the diagonalizing matrix are such a set.

In general, if an $n\times n$ matrix has $k$ distinct eigenvalues, then there may in general be anywhere between $k$ and $n$ linearly independent eigenvectors.

For any of this, it doesn't matter whether or not the eigenvalues are non-zero.

If $\vec v$ is an eigenvector, then so is $t \vec v$ for all real $t$. If they're asking about linearly independent eigenvectors, then you're right, but if they're just asking about eigenvectors, I would say the min and max is always infinite.