Multivariate probability density and distance... help!!

Hi all. I'm far from a stats connoisseur, and will probably use all the wrong words and describe my problem poorly. But I've got to figure it out and literally any help or direction would be greatly appreciated.

I've got a set of observations, each consisting of seven two-dimensional values. So each observation looks something like this:

(58, 73)
(114, 97)
(34, 116)
(59, 37)
(83, 115)
(23, 91)
(77, 66)

Also, I know that the points depend on one another in various ways (e.g. no two points can be too close), so we can't assume independence.

How can I characterize the probability distribution of a set of observations like this? I am getting particularly bogged down in trying to understand how to deal with a set of two-dimensional points: Can I simply treat each observation as a 14 dimensional vector, or do I have to retain the 7x2 shape of the data?

Ultimately I'd also like to measure the distance between individual observations in addition to characterizing the distribution, but when I use multivariate distance measures like mahalanobis I still run into this question about handing a set of points.

Please please please any help would be great. Thanks so much!!