Try to talk to the people you owe money to and ask them to lower your payment. If they say no, you might have to file for bankruptcy, which basically wipes out all your debt and you get to start fresh.
For your mental state, you have to start trying really hard not to think about all the negatives. For example if you're going to bed, you're in a safe and peaceful place, you can put all the worries on hold and deal with them later. Do you still have your job, if yes that's a pretty good thing, if no, might need to find one. Transportation wise, you may be able to take public transportation.
About your heater core, can you still drive the car and you just don't have any heat or does the coolant spill out?
Not sure what to do there, I guess you have to save up money to pay to get it fixed or possibly look up on youtube how to fix it yourself. Maybe there is a way to cap off the hoses that go to it so you can at least drive the car.
No matter what it is, things change over time. Imagine you could teleport 1 or 2 years into the future and perhaps those problems are no longer problems then, so you might have to tough it out and try very hard to get things taken care of.