Cannot download files or change settings

By troubleshooting steps, I mean things like starting Firefox in Troubleshoot Mode, checking whether the problem happens with extensions disabled, and trying Firefox’s profile or settings recovery options. Since you cannot download files or change settings, I would first try Help → Troubleshoot Mode. If the problem still happens there, the Firefox profile itself may be damaged or have a permissions problem.

I would not uninstall Firefox yet. Backing up your Firefox profile first would be the safest way to protect your bookmarks and other saved data.

Tried Troubleshoot Mode with the same results - No Download (Save) possible.

It's been so long since I first started using Firefox, I have no idea how to check for Profile damage or Permissions issues. Back to you, sir.

There seem to be some missing permissions necessary for Downloads folder in recent macOS versions.

You can either look in System Settings if you can grant Firefox the disk access permissions, or try changing the checkbox whether to ask for download location or not, and see if the system prompts for the permission that way?

To "jbr" and "malcomparked" - thank you for your suggestions!

I had to go 'around my elbow' several times with the help of Apple Tech Support in order to untangle this mess - but it worked.

I had to reinstall Firefox cleanly. I also had to delete numerous "Unsupported" file types from my Firefox history. Permission verifications were in my Mac settings and I would not have found them on my own.

Thankfully, my Apple agent took the time to walk me through resolving the Download issue, despite the fact that it was with a third-party (Mozilla) product.

Again, thanks to you both.