An irreducible polynomial P(x) of degree m over GF(q) can be used to construct an extension field of GF(q). What is actually meant by constructing an extension field?

and why is it important to ensure whether a monic polynomial of degree m over GF(2^n) is primitive???

lastly, there are 3 bases of finite field: polynomial, normal and dual base. in what condition each of the bases is favored over the others?

thank you very much for your help