The bias $E[\hat{\theta}_n] - \theta$ is exactly zero for all $n$.

The variance $Var(\hat{\theta}_n) \to 0$ as $n \to \infty$ and the bias $E[\hat{\theta}_n] - \theta \to 0$ as $n \to \infty$.

The estimator follows a normal distribution for all $n$.

The estimator is the maximum likelihood estimator (MLE) regardless of regularity conditions.