As for a), no. Permissions are a function of the underlying *nix OS, not a file manager option. And why would you want that anyway? Talk about a security hole.
For b), I don't know. That depends on how Nautilus handles it's file associations. Most file managers work by mime-type, though, rather than filename, so probably not. And this is as it should be, because filename extensions are a terrible thing to rely on when determining what a file actually is, and *nix doesn't generally do that.