My answers to your questions are assuming that Texas is not going to re-prosecute your son. Even though the case was overturned (which is rare) that doesn't mean that Texas can't try again. These are two different issues.
You have a bunch of questions here: Let me take them in order you present them:
1. Can your son be compensated for a wrongful conviction?
Generally yes in most states. Contact the Texas office for the appellate defender or a private criminal
defense attorney's office for further detailed information on the mechanics of presenting suit or a claim under state or federal law (typically known as a section 1983 claim).
2. What is his recourse?
The legal recourse for the damage to his reputation and loss of his liberty is a possible money judgment which I acknowledge is a poor substitute.
3. Is there grandparent visitation rights?
Yes, you may petition a court to allow visitation however the actions to accomplish visitation are complex.
In 2000, in the case of "Troxel v Granville", the Supreme Court of the United States decided that the law of the land does not exactly or automatically provide a 3rd party or a grandparent visitation rights and that state law must meet certain conditions before allowing a judgment to afford grandparents visitation. The circumstances under which grandparents could seek visitation time, and the amount of grandparenting time granted varied from state to state.
The Court in Troxel made clear (despite a plurality opinion (no consensus opinion) that there were certain prerequisites that grandparenting time statutes must meet in order to be constitutional. While there can be significant divergence of opinion with regard to what Troxel means, many lawyers believe that it requires that most statutes created or amended after Troxel (decided in 2000) will require first that there be some form of break in the parent-child relationship and that the grandparents provide "clear and convincing evidence" that grandparent visitation is in the best interests of the grandchild.