Quote Quoting abalone76
If I file for bankruptcy because of the need to pay rent on the previous lease, what happens to that situation? Is the landlord reimbursed from my assets until such time as he re-rents the property?
Any balance owed would be subject to the bankruptcy proceedings. If you remained in the apartment, it should be expected that any subsequent rent payments would be payable as they become due.

Quote Quoting abalone76
Also, I have a loan out on a car, and hardly any other monetary assets. I'm assuming the car would be taken, but if I'm still owing money on it, what happens in that situation as well?
If you surrender the car, it will be taken. If you want to keep the car, you would have to keep making payments. In Chapter 13 bankruptcy, you might be able to get the car revalued, such that the debt is reduced to the actual outstanding value of the car (if you are "upside-down" on the car - that is, owe more than the car is worth). That will change in October, along with many other aspects of bankruptcy, so now is the time to consult a lawyer.