Has Tyler managed this situation well? How could he have managed it differently?
What is at stake if Tyler simply accepted Jayden's friend request?
What is at stake if Tyler had simply ignored Jayden's friend request?

He did manage the situation well.  

Explanation:

A healthcare provider is not responsible for the emotional immaturity of a patient (recommended read: Boundaries by Henry Cloud and John Townsend). He could have explained to the patient's parents what occurred so they were not confused or better yet could have refused to talk to the 16-year-old privately altogether. Maintaining a professional relationship with patients is paramount (in most cases) as a healthcare provider. Allowing a minor to follow you on social media is inappropriate and may backfire heavily. If Tyler were to accept the friend request he would also open up liability to report any life-threatening psychological posts that Jayden may make seeing as many healthcare providers are mandatory reporters of these sorts of things.