Steve She is very open about talking about her sex life with her friends, so she wants me to be open about my chastity with em. Of the three points its my biggest concern. While she assured me they will keep it as a secret, i am still bothered.
I mean, there are multiple reasons to talk about that. If she intends it to be a humiliation challenge, by all means refuse unless you are into that. Do not let yourself get blackmailed into doing stuff you would rather not do.
But on the other hand, that does not seem like the way you describe your friend / potential girlfriend otherwise. I think she wants people to know about the arrangement you two have, so you have someone to confide in and someone can hold her accountable. And she does not want to tell otehrs behind your back. In that case, confiding your arrangement in people that are closer to her than to you might just be a way to shine a light onto this special relationship.