Go into my stuff and then preferences. All the way down the bottom you can click yes or no for hide from who's online. I believe that is how you do it.
I don't think you can clear the website without clearing the entire history. You should set him up as a different user on your computer. As the administrator of your computer, you can block certain websites. He will have his own history and you should be able to access his history as the administrator.
When I want to be invisible...I just say in a gruff voice with tears in my eyes, holding a chocolate bar: YOU CAN NOT SEE ME, I AM NOT HERE, LEAVE ME ALONE and then walk off with a box of tampax.