When the NTSB arrives, it's usually with the FAA in trail. The FAA is a party to NTSB Investigations.

Perhaps the pilot (or employer) decided a lawyer was a good idea due to the cargo being carried? Or the location of the crash into the ever-present schoolyard full of children.

You can make the investigators as mean or as gentle as you like. The nicest investigators can turn into the most forward and in-your-face interrogators if need be. Is your pilot fearful of what happened? Does the pilot have something to hide that the investigators might have seen in the wreckage? Or did the post-impact fire destroy the evidence?

As far as the medical goes, that's probably a distraction not needed in the book. Sometimes the FAA will want a re-exam ride and that requires a medical, thus the pilot will be grounded. Or, the pilot realizes he won't be qualifying for his commercial medical again and allows his to expire, to take up sport flying after his injuries heal. Everything is a process and even if the FAA wanted to do an emergency revocation of certificates, the paperwork takes a few weeks to months.

The investigators could ask questions whenever they want. They'd direct the questions to the attorney, if there is one. The attorney would make it a more adverse process, but, no matter, the investigators will ask their questions. The pilot could get a call with questions months after the initial investigation.

What are your characters telling you?