Let $BG$ is classifying space of $G$ topological group.

If $G$ is any compact group and $H$ is a closed subgroup of $G$, then the inclusion map $i:H\rightarrow G$ induces \begin{equation*} G/H\rightarrow BH\rightarrow BG \end{equation*} a fiber bundle?

If $G$ is any compact group and $H$ is a closed subgroup of $G$, then the
inclusion map $i:H\rightarrow G$ induces

\begin{equation*}
G/H\rightarrow BH\rightarrow BG
\end{equation*}
a fibration?

If $G$ is any compact group and $N$ is a closed normal subgroup of $G$, then
the quotient map $\pi :G\rightarrow G/N$ induces

\begin{equation*}
BN\rightarrow BG\rightarrow B\left( G/N\right)
\end{equation*}
a fiber bundle?

If $G$ is any compact group and $H$ is a closed normal subgroup of $G$, then the quotient map $\pi :G\rightarrow G/N$ induces \begin{equation*} BN\rightarrow BG\rightarrow B\left( G/N\right) \end{equation*} a fibration?