K9 filters based upon the Internet connection, not the browser. It will filter IE/Chrome/etc.
With YouTube, it is realistically all-or-none (in theory, you could whitelist some, but it would be very long, protracted, flaky and annoying).
With regard to lingerie sites - not really. This is because there are many sites that will not be flagged as inappropriate. There is always "block all except" - but I suspect that it would not really work. I mean - you can't even block all disgustingly inappropriate sites - it just takes a new one to pop up! You can set filter strength to highest, cut out everything, and then add categories as needed.
What I tell my children is that I can see everything that they do, and I've shown them what they've done. This in itself goes a long way.
At the end of the day, it's like a lock on a door. And the crucial thing to remember about locks is that their raison d'?tre is to be opened.