I am only somewhat familiar with the subject, but I will an attempt to answer your questions as best as I'm able.

1. A very simply measure of similarity between two random variables X and Y would be the covariance, i.e.

Cov[X,Y]. An feature of this measure is that it is (bi-)linear, i.e. for random variables X, Y, Z, and real number a,

Cov(X+aY, Z) = Cov(X, Z) + aCov(Y,Z).

The correntropy of two random variables X and Y is

Correntropy(X,Y) = E[K(X-Y)]

where K is a kernel function. This measure generally isn't linear.

2. Yeah, it seems the values should range from a11 to a1m (a21 to a2m). Looks like a typo.

3. No idea, sorry.