My sheer guess is that no they cannot take your car. Never heard of that happening. Even in bankruptcy they let you keep enough stuff so you can still survive and make a living, etc. Again, just a guess.
Now, I am a bit surprised to hear you say that they can't touch your Social Security benefits... I would think that they could still levy your account for a few dollars a month.
When you show up to talk to the judge (and DO show up!) just explain your situation and tell him you'd gladly work out to pay $10 a month.
As for "Do they have to accept any payment... No. It's their debt, they can do what they want...