With regards the Category table lists - they're manually added, which is why there are some missing. If a given eg, Sword, has Category:Swords added to its item page, it'll appear in the alphabetical category list at the bottom of the page. You can sort the table alphabetically to see which ones are missing and add them.
The issue springs from editors making new item pages and there being a plethora of other pages that an entry for the item could appear on which aren't then updated (eg type category, ability/skill bonus, obtainment) - likely because the original editor never uses those pages and is unaware of them, but also possibly because they don't want to take the time to update in all of those places. The only thing I can suggest is if you see something missing, edit it in.
Regards a gear database, I'm open to suggestion, but not sure if its possible for a wiki to do. I'm thinking it'd be a dpl page with item data organised in templates, but with about 13k weapons + armor, it's a huge nested function needing to run each time the page is loaded (it's why straight databases are better).
I actually have my own spreadsheet outside the wiki, taken from the code and updated each month, with jobs and flags split out so that it can be easily filtered and sorted for the purpose of considering gear. I think I got used to having that info when ffxi.somepage was running, but nowadays the same functionality is also available over at ffxiah.com with the advanced search.