Sterility is more of an issue here than anesthesia. The implant is in an area that must be kept very sterile during its insertion. An operating room is the most sterile place to perform this. As far as anesthesia goes, it may be painful to do just under local. Therefore, I would recommend at...
With respect to the receding chin, there are multiple issues going on here. The receding chin can be augmented with a chin implant, but it is probably best to wait until he is 18. If he is sleeping with his mouth open, that indicates that he may have a deviated septum and will require nasal...
A chin implant and possibly fat grafting along the deficient mandibular border will likely improve your facial symmetry significantly. A consultation with a qualified plastic surgeon is the next step in figuring out a plan specific to you.
