For many types of high pressure purchases in NY there is a 3 day statutory right to rescind, but not with auto leases. I would suggest you contact the dealership and/or leasing company and explain that the disposition fee was not brought to your attention and that you want it waived. You may file a complaint with the NYS Attorney General's Office if you reasonably believe this was a deceptive trade practice, although that claim may fail if the disclaimer language in the "no money down"...
As a general rule, continued violations of a contract do not make the whole contract null and void. However, if you have consistently failed to assert your rights when the contract was violated, you may have waived your rights under the contract to complain about similar violations in the future. Many contracts contain non-waiver provisions that protect against this implied waiver. So, as my colleague aptly stated, it really comes down to a lawyer reviewing your contract and applying the facts...
Get documents evidencing the mistaken identify problem and show them to the prospective employer. Even if you don't get this job, it will help if this comes up again. In fact, you should consider doing a background check on yourself and showing that to the prospective employer.
If you value your job you should get a lawyer involved asap. The lawyer can send your employer a letter of representation and minimize your employer playing games with you since they will know their conduct is being scrutinized. It will be easier for you not to get fired than to regain you job. Act quickly.
I think we are assuming you own your home. If you rent it, you can take action against your landlord in addition to what has already been suggested. Speak to a landlord/tenant attorney if you are a renter.
I agree with the others that without proper modification to the lease you are bound by it. My concern is whether you are still responsible in the future. How long is the lease? If you are still responsible for rent and your roommate pays it, expect to get sued again. If you are still on the lease, get with a lawyer and review how you can get out of it.
As has been stated, the circumstances of your termination play a role in determining the ramifications of your employer banning from future employment after agreeing in writing to not do so. Was your resignation (which will result in you not being eligible for unemployment benefits) given in exchange for the non-ban promise?