If you want to get some reliable suggestion from some folks here (or even lawyers), you have to lay out a complete story.
The evaluation report and the judge referring him to the hospital points toward either he was on drugs or he was on mental state. I believe he could not respond to what they asked him properly. Even the story you have laid out getting arrested at 4 AM suggests he might not be in good state of mind during that time or not sure at present too.
1. "One day he just left..." do you mean he left just to go and chill out around the city or left in the sense that even he didn't know where he was going. Where was he going at that time?
2. "asleep in the cab.." did he tell the cab driver where he was going? if he had told the cab driver the destination and that would come out to be say 20 dollars fare and the cab driver kept driving while he was asleep, then the cab driver can be sued. However if he told the cab driver to take him around till he says to stop, then cab driver is at no fault.
3. "calling cops and getting arrested part" ....the cab driver wouldn't simply call cops while your friend was going to the ATM since the cab driver was getting easy 150 dollars for a simple trip. Did your friends say that he wouldn't or couldn't pay? Could that be a reason? You said even after cops came, they gave him a chance to pay. He had no phone at all or he had no numbers of any one? So he came to you in Austin from Michigan without any phone contact? No number in his phone? He could have simply called the bank (phone number on the back of his debit card) to clear his card for withdrawal, or he could have told the cab driver to take him back to your apartment to be able to pay. Of course the cops would arrest him if he is not paying at all. Lots of things should have happened during that time for cops to arrest him.

Either your friend or you are hiding lots of information.
Even if you arrange a private lawyer, you have to have answers to those concerns.