I have handled cases like this before... there are 2 possible legal theories. 1) did Riker's have notice that the other inmate had violent propensities? Did your husband complain about him before the attack? Had the person assaulted others before the attack? 2) The second, and harder theory, is that there was insufficient security. Your husband needs to serve a Notice of Claim on the City of New York within 90 days of the incident in order to preserve his right to sue.
You can subpoena the doctor (and pay the subpoena fee) and elicit fact testimony. However, you cannot force a doctor to give expert testimony without paying an expert fee. The rule of thumb is that you never want to have to subpoena your own doctor.
You can get some info here:
However, it is not comlete as not all medical malpractiec settlements are reported.
You can also try the Office of Court Administration web site and see of the doctors have been parties to lawsuits.
You do not have a medical malpractice case unless - at minimum - the delay in diagnosis made a difference. Would your treatment have been the same? Why do you think you contracted it at the gym? The gym could be liable if it had notice.
The DWAI will appear on your RAP sheet (criminal history) so the DA will take it into consideration. It is highly unlikely that the DA will offer you another DWAI. Perhaps a program is in order and something the DA will consider. Hire a really good lawyer.
There is potential liability. It depends on whether Starbucks had actual or constructive notice of the uneven tile and what the height differential was. Whether to pursue a case will likely depend on how the burns heal and whether you end up with permanent scarring.