Apparently my computer is infected by Provider adware. At least Mozilla is. I have no problems on other browsers.
Malwarebytes, AdwCleaner and Ublock Origin don't seem to detect nor block it. I have re-installed Mozilla, but the adware is still there. Also, the most comprehensive scan my Malwarebytes version (Home (Premium) 2.2.0.1024) has to offer, which is apparently the latest free one, only lasts for about 15 minutes, hardly the whole night. The scan is simply called Threat Scan, and there is no Deep Scan as there used to be. It has found a few PUP-s, but neither of them was Provider and removal of all the PUP-s hasn't solved my problem.
Is it possible that Provider is in the official Mozilla download site? It doesn't provide an EULA.
Or am I using Malwarebytes wrong?
PS: Mozilla retains its bookmarks and history when I re-install it. I assume it auto-saves backups. Is it possible that it does the same with Provider?