In earlier times, he was a good friend and traveling companion of Baron Klaus Wulfenbach's, and presumably of the Heterodyne Boys as well. Now since both are older and saddled with responsibilities, he is "merely" a good friend of the Baron's with little room for travel. This familiarity allows him to retort to Klaus's demands from his hospital bed with no fear or intimidation whatsoever, and in fact he will bully Klaus back for his .
From Gil's to the doctor, Sun seems to have had some hand in training Gil in medical sciences, as "sifu" means "master", "teacher", comparable to the slightly more familiar Japanese term "sensei". Dr. Sun also mentions that it's been a while since he gave Gil ; this may imply that Dr. Sun's title of Sifu is for martial reasons rather than academic, and that he may have instructed Gil in a far more physical set of classes.
The doctor runs the Great Hospital with strictness, great efficiency and excellent hygienic practices; his unorthodox experimentation usually produces beneficial results for his patients.
In addition to his considerable medical skills, the good doctor appears to be a capable physical warrior, able to make Klaus worry about the continued existence of his Medical Transport Clank, apparently for . This is in addition to being confident enough to plan to give Gil and to feed DuPree her own arms.
He is probably currently trapped inside the Mechanicsburg time-bubble, but there has been no explicit confirmation of this.
The print novel Agatha H. and the Voice of the Castle notes that Sun did indeed adventure with the Heterodyne brothers and Klaus, and left his homeland China after somehow incurring the wrath of that country's Emperor.
Possibly relevant outside information
Dr. Sun shares the name "Jen-djieh" with Judge Dee, historically a famous Chinese magistrate and minister, legendarily a hero of operas and ancient mystery novels, and eventually the protagonist of a mystery series by Robert H. Van Gulik, a Dutch diplomat and Sinologist. The transliteration (now archaic) is the same used by Van Gulik. The characters used for the name are "benevolence" and "prominence".