Let $M$ be a topological manifold with a continuous, free, and proper action of a topological group $G$ on $M$. Is $M/G$ a topological manifold? Is $M \to M/G$ a locally trivial principal bundle?
If no, are there mild assumptions on $G$ in order to ensure $M/G$ is a topological manifold and/or $M \to M/G$ is a locally trivial principal bundle? By "mild" I mean that $G$ is necessarily not a Lie group. I am aware that "upgrading" $G$ to a Lie group allows us to "downgrade" $M$ to a completely regular Hausdorff space to ensure that $M \to M/G$ is locally trivial.