I am reading notes of Michel Brion on spherical varieties.

Consider a reductive group $G$, a Borel $B$ in $G$, a finite dimensional $G$-module $M$ and a closed orbit $Y$ of $G$ in $\mathbb{P}(M)$. The stabilisator of every point of $Y$ is a parabolic subgroup of $G$, so we can fix a $y \in Y$ such that $By$ is open in $Y$ (by Bruhat-decomposition). Also choose $m \in M$ such that $y=[m]$.

My Question is first of all: why is there an $\eta \in (M^\*)^{(B)}$ such that $\eta(m)=1$. And why are the parabolic groups $G\_{[\eta]}$ and $G\_y$ opposed?