Hi,
QuoteXML error: Could not register node named "HatBase" in mod Core because this name is already used in this mod.
can it be that you recently update Rimworld from a pre 1.0 version to 1.0 ?
Then delete the Core folder under mods and let steam repair the installation or unzip it again if you use the (DRM-free version).
That should fix most of the error's.
If you still got error's after that, post a new log-link.