I don't want to be Debbie Downer but what you're describing is gross. Having to scrape the poo off the carpet? How long did you let it sit there?
And you've already gotten in hot water for dog urine.
I wouldn't call this eccentric, it's poor hygeine.
Having a diapered caged chicken in your house as a pet or because it's ill or injured is one thing, having a grown Rooster did you say?- running around the house and doing his buisness everywhere is really nasty. Do you realize how many germs are in feces, let alone bird feces?
Please, Please, PLEASE for the sake of your health and if you have children living in that enviroment, CLEAN IT UP.
Put the bird in a cage or force it to wear a diaper. You're bound of get sick and you may have already and just not realized it, any bout of stomach upset or anything you or your family has experienced could be due to bacteria from chicken poo!
There is a reason that chickens are livestock hun and I really do not want to be mean or anything but you're playing with fire! Some of these bacteria or diseases can kill!
Also, I just have to throw it out there that while he may be cute, or was as a cute, may be extremely affectionate or friendly. He is an animal. Chickens are not solitary animals, if he is a Rooster, first of all I have no idea how you plan to keep him quiet in an apartment, but secondly, as he sexually matures you could be in for drastic and not so nice behavioral issues, flogging, humping, even flat out attacking people.
A full grown Rooster can take a childs eye out and they tend to go after people when their backs are turned. Some very friendly roos can turn!
He is BOUND to be lonely and one very confused chicken.
For his well being what I would do is please try to find a local farm with other chickens where he can go. If he is very handleable he may be perfect for some teen to show in 4-H or something. But he needs to be with other chickens in order to be a happy well adjusted chicken. If you love him your best bet is to let him go to somewhere he will be happy and be able to do normal chicken things like dust bathing, watching over a flock of hens, being in the sun and grass, etc. This goes for a hen as well, they all need companionship and I am NOT telling you to go out and get another chicken.
If I were you I would rehome him and steam the carpets, and then maybe hire a dog trainer to help with your dog.