(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.

(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.

Edit: The original source for the result is a paper of Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57, (1953), 115–207.