Cannot save/edit categories or permalinks

Summary of my problem – I really hope I get a reply as I’ve Googled and posted and researched and keep hitting a wall:

1) Created a page called blog and then made “blog” the parent category for all of my blog categories.
2) Deleted parent category called “blog” and wiped out the categorization of all my posts. Woops. Do I need a parent category called blog anyway?
3) Tried to add back individual categories but WP 2.5 won’t “let” me b/c the old cats are still there … you just can’t see them in Manage Categories UI.
4) Can add “new” (never been added prior) categories. But only sometimes. Other times WP won’t let me add them.
5) Permalinks cannot be edited in the Write Page interface no matter how many times I click Save.
6) Permalinks look wacky with things like 2 trailing slashes depending on how I set the URL for my blog as well as how I set up permalinks.
7) Part of the wackiness is that WP is automagically appending things like -blog to my category slugs. What the?! So a new category slug might show up like this: https://www.mysite.com/blog/internet-marketing-blog-2

Another question: if my blog is “inside” my WP CMS (static front page called home), should my Blog URL be https://www.mysite.com/blog or https://www.mysite.com? And do I need a trailing slash? (All my WP files are in the root directory.)
Karri