I feel I have to repeat it for the fourth time:
I want to turn web browsing control off, but leave parental control on, e.g. for time restrictions.
This can be disabled globally by disabling "Web antivirus". However accounts with parental control have it enabled even when I explicitly disable web browsing for them.
This has NOTHING to do with browser setup, only with KIS set up.
Also: you should understand that HSTS means "HTTP Strict Transport security" which means that no security certificate (including KIS) will be accepted, except google's.
That would require browser plugin. Fortunately,it existed in previous KIS versions even for seamonkey, because it's mozillabased, so firefox plugin worked. Unfortunately, it does not seem to be available now.