Sir Ronald Fisher introduced the method of maximum likelihood estimators in 1922. He first presented the numerical procedure in 1912.

The likelihood has to be maximized numerically, as the order statistic is minimal sufficient

Maximum likelihood estimators of the Cauchy distribution cannot be written in closed form since they are given as the roots of higher-degree polynomials. Please see the link for details.

The answer depends on what variable the maximum likelihood estimator was for: the mean, variance, maximum, median, etc. It also depends on what the underlying distribution is.

There is simply too much information that you have chosen not to share and, as a result, I am unable to provide a more useful answer.

Negative numbers are numbers less than zero.