I would email her and tell her exactly what you said about your business. If you care at all whether she will be upset. If you are not bothered if she will be upset, just do it and don't say anything.
Depends on what kind of friend she is. People can have major character flaws and still be friends, although it does not mean you have to accept those flaws without comment. But if this is a flaw you cannot deal with, or not prepared to accept, then you should press un-friend.
and I don't have any 'facebook friends'. All my friends on facebook are those friends I have in real life who I talk to online via facebook when I don't see them. I would struggle to just get rid of someone whose opinions i did not like without hesitation.
But I know some people have hundreds and hundreds of 'friends' who they don't know.