Hello and thank you for your question. What state are you in? It shouldn't make a difference but I always like to know what state people are in because answers can be different. Generally speaking, the answer will be the same no matter where you live in the US.
Please note: The answers provided here do not, under any circumstances, create a lawyer-client relationship and are provided to supply a general answer based on the facts as given by the author. The attorney is not giving advice but is answering the question in general terms. At all times, the above attorney will advise the author of the question to seek independent legal counsel. The above answers should not be relied upon by the author or by anyone else for the authoritative answer to the question. Consult with your own lawyer for your legal questions.
This landlord is indeed the worst and should be made to pay for what he has done. In almost every state, landlords are required to render a place they are renting in habitable condition, which is called a warranty of habitability. They cannot allow holes in the floor, feces in the apartment or rental, and if it is not fit for human living it is not habitable. Your landlord is violating the habitability statutes in your state. Even states which do not have strong habitability statutes in the state still have laws on the books where they cannot allow feces, toxic smells, and some states specifically provide that there cannot be mold. When there are rodents, that makes the place uninhabitable. You have so many habitability violations here. I am so sorry you are living in this condition.
There is something you can do about this. If you want to stay there, you may want to bring your landlord to court, and you should be able to do that. He cannot make you sign a contract that he's not responsible for anything. That is not acceptable. He cannot "contract away" his duties to provide a habitable place for you. The contract will generally be held to be null and void. Nice try landlord, but, no. It's not legal for him to do that!
Electrical issues, sink issues, mold issues, hospitalization -- get receipts for medical bills, etc. -- the loss of your dog -- this is just sad and I'm so sorry you're going through it. He cannot just make up whatever contract he wants to. It is illegal to get someone to agree that he is not responsible, because he is!
I suggest you see a local landlord-tenant attorney or an L&T attorney in a nearby big town or city. That attorney can tell you about bringing a legal case against the landlord for money damages. Also, the L&T attorney can let you know, under your state's laws, whether you can leave, based on what is called constructive eviction, and therefore refuse to pay any more rent, or what remedies you have. Some states allow constructive eviction, and some do not. Speak with a good landlord-tenant attorney in your area. Find someone who has been practicing at a minimum of 10 years and ifyou want some names of landlord-tenant attorneys in your area I can send them to you. However, please note : I do not know any of them personally and I cannot vouch for them. I do not know if they are any good but I can certainly give you a list of names and then you can choose who you want.