It sounds as though you have some malware or prank software. It could be an add-on, or it might be external to Firefox.

Let's start here. Open the following page and disable ALL nonessential extensions. By nonessential, I mean you cannot use the internet without it.

orange Firefox button or classic Tools menu > Add-ons > Extensions category

Then restart Firefox and test again. Any improvement?

I assume you run full-time security software. These two free tools are highly regarded for supplemental scans for anything your regular software might have missed:

Malwarebytes Anti-malware : http://www.malwarebytes.org/products/malwarebytes_free

SUPERAntiSpyware : http://www.superantispyware.com/

I'm just a regular user here in the forum, but that sounds like it could be a virus or malware that you may have acquired while using FF and maybe it changed the settings only for the browser you were using when you acquired said malware. Try running a full system scan with your antivirus program, or do a scan with MalwareBytes Anti-Malware and see if it finds anything.