Is it possible to be sent to a line/infantry unit as a medic after last duty station was TRADOC?

All the FBI cares about is a bachelors degree. They mostly don’t care what the degree is in, but they prefer accounting type degrees. For the most part, they will train you on what you need this know. Whatever military experience you have is a wash. It’s better than no military experience. But they honestly don’t care what you did in the military. I know this from 30+ years in LE and working with the FBI and having friends in the FBI.

If you become an MP, you'll need to try to become CID later on in your career. You'll need a 110 GT score on the asvab for CID and your going to want to get a bachelor's degree in accounting for FBI.

You can absolutely be attached to Line Infintry, Cav, or MP as a medic.
FBI is okay with MP, but they like combat arms/maneuver branch background (Infantry especially, but the others work too) as a general preference as an enlisted background.