she is broody thats one thing for sure and if she isn't come out of the coop I would bring her food and water every day but about the marking of eggs I don't know about doing that but I wouldn't take the egg. how to find out if they are fertilized is easy after 2 weeks you can take a flash light up to the egg and If there is a shape in it then it is fertileize abd if not then it isn't I hope this helps