Is chewing gum allowed during ramadan?

I'm not actually muslim, but I respect the religion. I'm just curious. and what do diabetic muslims do during ramadan? I know that an occasional date is supposed to be permissible but i still don't think it could be done in a way healthy to a diabetic. and I read somewhere that women can not entirely fast when they are menstruating. Is this true? Why? and would that mean that the women would have to share they are menstruating? I would think that would be embarring/ a little against what the Qu'ran teaches about women's modesty. I apologize if any of these questions are offensive, I don't mean them that way. I just think too much. I'm very interested in learning about other religions and appreciating what they have to offer while being respectful to other's beliefs.