You're not using Private Browsing mode, are you?

I have it set to 'never remember history' and 'tell sites I do not want to be tracked' but when I close and then re-open my browser, sites have my password saved

'never remember history' is permanent Private Browsing, no history is saved.

Those Saved Passwords were probably saved when you weren't using Private Browsing; the prompt for saving a new password doesn't appear in Private Browsing.

If I switch it to custom setting I still can't access the 'clear history'. Right now, the only way to turn off passwords is to log out of the site.

Does "Always use Private Browsing mode" have a check mark?

So, I ended up making a change, closing the browser, and opening it again, making a different change, closing the browser, and so on.

I was eventually able to access 'clear history' under 'use custom settings' and check it, though when I re-opened the browser it wasn't checked. This happened several times. I did the same thing over and over until I was finally able to check box and it has been staying checked, but I have no idea why it worked that time. I'm keeping my finger crossed that it stays that way.