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Re: Symbolic tensor analysis in Mathematica 8

first question,
if I understood correctly, your answer is something like this:
Dim = 3;
V = Table[v[i], {i, 1, Dim}]
in this way you creates a vector with v[1],v[2] and v[3] as components.
second question:
In this way you can, for example, also define it with a loop for:
V[[i]]= "what you want" 
To tell to mathematica that for example v[1] is a function of x,y,z you can use two way.
I suggest to use this one.
v[1]=x^2+y^2+z^2 (for example);

I wrote for you this very simply example:

Dim = 3;
V = Table[v[i], {i, 1, Dim}];
V[[1]] = x^2 + y^2 + z^2;
V[[2]] = x^3 + 4 y^3 - z^2;
V[[3]] = x - y + z;
D[V, x, y, z] 
the last line evaluates the total derivative of the vector V .If you want the partial derivative 
D[V, x] respect to x
D[V,y] respect to y
D[V, z] respect to z


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