How can I measure if a population has the same distribution as other?
What I'm gonna say might seem too simple, but I assume, it might not be bad to fit a multivariate distribution (like Gaussian) to each distribution and then figure out what the mean and covariance matrix are. Mean might not depict so much information but the variance and correlation that are exposed in the covariance matrix might be helpful. 

For the case of determining if a variable is useful or not, analyzing its correlation with other parameters might turn out to be useful. 

(These are my own thoughts)