Reference for Hodge decomposition for flag variety

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$ .