These are very unfortunate circumstances and I am truly sorry to hear about the unreaonable demands being placed upon you. However, as you correctly state, as a salaried exempt manager you can be required to work whatever number of hours your employer determines is necessary for you to get the job done. Furthermore, as a salaried exempt employee, you do not typically have any entitlement to rest or lunch breaks. A good employer will make their employees' hours reasonable and will allow them the opportunity to take necessary breaks. This is simply good management because if an employer doesn't treat their employees well those employees will leave, creating high turnover and ultimately harming the employer's business. But there is no law that requires employers to manage their business well, or which prevents them from running their business into the ground with poor management tactics.
Your only recourse in this situation would typically be to try and negotiate better terms of employment under the threat that you will resign if conditions do not improve. If conditions can't be changed, you can also try to negotiate greater pay. Ultimately, though if the terms of employment being offered to you continue to be unacceptable, your only remaining option is to quit and look for other work. The fact you signed a lease is highly unfortunate but does not somehow change the law with respect to your employer's obligations to you.
Technically, it might be possible to quit and collect unemployment benefits on the ground that no reasonable person wpuld have continued working under these circumstances. However, there is always a risk you will be denied and so the better course of action if you do intend to leave this job is to wait until you have secured another offer of employment somewhere else. It also tends to be easier to get hired when you already have a job, so this work in your favor anyway.
I hope that you find this information helpful and am genuinely sorry if it is not what you were hoping to hear. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
If you do not require any further assistance, please be so kind as to provide a positive rating of my service so that I may receive credit for assisting you. Very best wishes moving forward.