If you are asking "Does he have to give us a complete bill showing all receipts for work done?" by statutory law, the answer is maybe.
If he is located within a county with a population larger then 50,000, Vernons Texas Civil Statute, Art. 9028 (Motor vehicle repair facilities; registration) can come into play. It applies to "a person that engages in the business of repairing or replacing the nonmechanical exterior or interior body parts of a damaged motor vehicle." As you can see, it applies to nonmechanical repair work, which should be sufficient for your restoration and while this particular statute does not require written estimates or return of parts, it is an often overlooked requirement and can often be used to 'influence' a repair facility to see things your way. You will also find that it requires certain records to be maintained, which may not have been not done.
The full text can be viewed at:
http://www.capitol.state.tx.us/statutes/vntoc.html
Before paying anything, I would strongly suggest that you talk with an attorney in your area. The amount of money you are talking about is sufficient to justify spending $100-$200 finding out what your exact legal position is.
Further, your post asked:
Q1) "What are our legal rights?"
A1) As noted above, there are too many variables (documents, agreements, phone conversations, etc.) for anyone not intimately familiar, to answer all of your possible rights. Talk with an attorney and he can review your facts.
Q2) "Can he sell the car?"
A2) Texas does allow provision for a mechanic to sell a car to recover their costs of repair. This is done via a 'mechanics lien'. Again, see a lawyer to protect your rights.
Q3) "Does he have to keep it safe (my fear is that it will be 'stolen') or damaged (it is a 60 T-Bird convertible)."
A3) He is under no special 'safety' or security requirements than is normally required to maintain the safety of a customers property. And in most cases, repair facilities have a 'no liability' notice posted on premises which could further dilute his responsibility.
Q4) "Does he have to give us a complete bill showing all receipts for work done?"
A4) Not unless he agreed to do so at any point in the repair.
