Will I need foot surgery for focal longitudinal split tear of the peroneus longus tendon, tenosynovitis of the flexor tendons, or a non visualized atf?

Peroneus longus. You don't state if conservative care was done. Always start with rest, immobilization , etc and see if the tear will repair. The tenosynovitis should respond , then, to NSAID or injection therapy. The atf may well heal with the same rest immobilization for the peroneus longus . Good luck.
MAYBE. For the flexor tenosynovitis, no; PT, rest w/ a boot, NSAID's may help. "Non-visualized ATF?" I would have to see you clinically. Do you have an unstable ankle? "Split PL tendon"-I would start w/ a boot or brace, maybe PT. If it does not get better and it hurts, may need repair. Good luck! Dr. Latva.
Probably. You can try some conservative treatment, physical therapy and immobilization. Your best fuctional result may be to have the pl tendon debrided and repaired. The tenosynovitis should be easier to address with either steroids or/and non- steroidal anti-inflammatories and rest. .
Depends. Many peroneal tears can be treated with rest, bracing or other forms of temporary immobilization plus a rehabilitation program. Surgery can be utilized if you fail conservative care. The lack of visualization of the anterior talofibular ligament means that the MRI slices were not thin enough to capture it or it has likely been injured in the past. Many function well with an abnormal atfl on mri.