I am looking for a reference that contains lots of calculations for specific examples of various objects one can associate to a reductive algebraic group. For example, given a (specific) linear algebraic group $\mathbb{G}$, I would like to know things like:

-a maximal compact subgroup of $\mathbb{G}(\mathbb{R})$

-the rank of $\mathbb{G}(\mathbb{R})$

-a Borel subgroup for $\mathbb{G}$

-the Lie algebra of $\mathbb{G}$

-a Cartan involution for $\mathbb{G}$

I assume these things are well known to people who study algebraic groups. I just can't find a place where specific examples are worked out (or even stated) in any detail. Thanks!