Various test of significance

Hi,

I've got a response matrix (Y) composed of multiple quantitative variables
of the same nature which I am subjecting to multivariate analysis. I was
wondering if there was a simple way of testing the following 3 things in
R:

1) Significance of the coefficients of correlation (from the computed
correlation matrix of Y).
2) Independence of the Y variables.
3) Multinormal distribution test.

Thank you,

Michel