category names not displaying in back end, plus more

I’m having some very weird problems. You can visit my site at https://www.uuca.org to see that none of the links work—everything is a 404.

However, if you go directly to a page without using a pretty url, it gets you right there.

But that’s not the weirdest part. If you go into my admin section/dashboard, and go to Manage>>Categories, you see the correct number of categories listed alongside the category descriptions, but no category name. It’s the same with tags and link categories: the correct number of items is there but no names.