I've lived in shared-living houses before with the cat issue twice and found roommates are usually pretty understanding and try to be accommodating with keeping their pets under control within reasonable limits (what you have posted sounds reasonable). Just talk to them about it frankly and let them you know don't mind that they have a cat, just that they respect your wishes and keep the cat out of your way.
I don't have any advice though for the duplex thing, that sounds like a pretty sucky double-standard but as long as you're living there I don't know what you could do other than try to talk to your roommates about your feelings. If it's that big of an issue, find another place to live I guess?