normality and cohen-macaulay condition I am not an expert in the geometric meaning of normality/Cohen Macaulay, so the following questions could seem very stupid.


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*Are there examples of connected varieties over a field whose irreducible components are smooth and they intersect in a closed of codimension $> 1$? 

*Are these varieties normal even if they are not irreducible?

*If the whole variety is Cohen-Macaulay, with smooth irreducible components, does this imply that they intersect in codimension $> 1$?

*In the cases where I have Cohen-Macaulay + intersection in codimension $> 1$, do I have normality of the whole stuff or I need also irreducibility?

*In general one needs normality to extend sections of a line bundle. Does the condition that the singular locus has codimension $> 1$ make it work also in the not irreducible case? By this I mean that I have a line bundle on these smooth components outside their  intersections and I want to extend it to the whole variety, possibly in a unique way.


Thanks

Consider $A=k[x,y]/(xy)$ and $X=\mathrm{Spec} \ A$. This is a connected variety with two irreducible components that meet in a closed subscheme of codimension $1$. (It's the union of the $x$ and $y$-axis in the affine place.) So that's not what you want in question 1. 
Let $X$ be a connected variety with irreducible components $X_1,\ldots, X_n$.
If $X$ is not equidimensional funny things can happen. For example, You can glue the affine line to the affine plane in one point. This is a connected variety of "dimension two". Its irreducible components intersect in a point. So this answers your first question, albeit in an unsatisfactory way because your varieties are probably equidimensional. (So the answer to q1 is yes.)
For your second question you can do similar things. Just glue a singular curve to a singular surface along a smooth point. The resulting scheme is non-normal, but its irreducible components intersect in a point of codimension 2.
