Well, to be fair about the college thing, if you're living on your own you usually get a free ride if it's community college. My friend has been on her own since 18. She moved out after saving up all through high school and she's almost 21.
It is possible.
If the car is in your parents name, they can claim it. They'd have to write it over to you and you would have to take on the insurance, if you haven't already. This is just all assumptions, for all we know the car is in your name.
You'd have to reapply for a new drivers license in your new state I think, and you'd definitely have to update your address, but I don't know how/where you'd do that. It can also be hard moving out if you have no one to vouch for you for apartment owners or house renters. ex, someone could rat you out/where you are etc. I think it's like 3 months usually down payment on anything and the cheap cheap apartments with no heat/water/etc usually go for like 650 a month, so almost 2 thousand down right there. That's just my area though, it could be cheaper other places.
If you really want cheap, probably you want something like a house owner with a 6-bedroom house essentially made to house several people. My friends and I met a guy flipping an old house basically made to have each floor be an apartment, and it fits 6 people. I don't recall the cost but it's 250/mo cheaper where my friend has lived since 18 so it's gotta be pretty cheap, all-included.
Basically, car could screw you up depending, you probably/might need someone to vouch for your maturity for an apartment, which can get hairy, look for houses made to have like 4-6 people living there, are it'll likely be cheaper at the cost of probably having to deal with the problems of living with 3-5 other people.
My friend was also told to be wary of leasing agreements. You can get bound to something and want out but you can't get out.
Also, he'd probably be able to get food stamps. My friend applied as it's getting hard and she and her boyfriend get 170 a month. I mean, at this age, if you work your ass off, you can live on your own, go to school, and eat. My friend works 24-36 hours a week, goes to school full time, and makes all her own payments for everything since she was like 16 (she's always paid for the car).