(1) Assuming you are referring to the coefficient field for your cohomology theory, then yes, the result immediately extends to $\mathbb{R}$ and $\mathbb{C}$ coefficients.

(2) Two sources are Fulton's *Young Tableaux* (Chapters 9 and 10) and Manivel's *Symmetric Functions, Schubert Polynomials, and Degeneracy Loci* (Chapter 3).  Both of these sources assume a basic knowledge of and familiarity with algebraic geometry.