Reference for Hodge decomposition for flag variety

Question

Any references for proof of the following facts:

1. The cohomology of the (complex) flag variety is always in $(p, p)$-type of Hodge Decomposition.

2. The natural map $G/T → G_\mathbb{C}/B$ is a diffeomorphism, where $G$ is compact connected real Lie group and $T$ is its maximal torus. $G_\mathbb{C}$ denote the complexification of $G$ and choose a Borel subgroup $B$ containing the complexification of $T$.