Finite Field

I have been away from algebra for a long time.

A finite field F of order can be represented as , where is an irreducible polynomial (in ) of degree n.

I remember that any finite fields of the same order are isomorphic. Also I remember that the multiplicative group of the field is cyclic. A few questions arise:

1) If I am given two irreducible polynomials and of degree n. Is there any quick way to explicitly find an isomorphism between the field constructed in the two ways?

2) If I am given , how can I quickly check whether x is a primitive element of the multiplicative group of the field? More generally, what property does satisfy in order to have x as a primitive element?

3) This should be an old question. How to count the number of irreducible polynomials over and with degree n?