Custom fields for category description

No, that’s not supported, and I wouldn’t recommend it: it means you’re starting to misuse your data model. Remember that a taxonomy is a simple term relationship to help streamline classification and searching, not something intended to hold extra data. Yes, this is my soapbox, but if you’re starting to associate data with your taxonomy (e.g. your category), then you’re no longer using it as a taxonomy. I would instead define a custom content type and then use that as a pseudo-taxonomy — define custom fields that reference the other content type.