Firefox v48.0.2
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OS X 10.8.5 Mountain Lion. (Yeah, I know it's ancient, but ironically I can do lots of things I can't do on my rMBP's running macOS Sierra. I know I need to upgrade, but I am so swamped with work and life I don't have time to migrate my 1TB of data off of my MacBookPro and alsofigure out how to keep my working applications working...)
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Being a privacy and security nut, I have been using the Open NIC Project for years, and choose DNS that offers no logs.
While sometimes those free DNS servers go offline or peter out, the ones I currently have work on this rMBP, so they should work on my MacBook Pro too.
And, as stated before, Google's DNS servers should *always* work.
I would never use an ISP's DNS or my hotel's DNS for privacy reasons.
But, changing your DNS settings would be for testing only, change back if that's no help
Will that erase important things like my Bookmarks, History, Settings, etc?
That file is used by Firefox in conjunction with the security certificates that web sites offer. When you rename the existing file, then re-launch Firefox, a new certificate file is created. There's a good chance that will fix your problem, and won't affect your usual security setup on your Mac, or whatever you use with your internet connection. That new certificate file should not affect anything else in your browser.