Height might or might not be an issue.
My daughter is 4'11". After starting flying she was vaguely thinking of being an airline pilot, I decided to test whether she could reach the rudder pedals in an airliner. After landing in a 757 when on a holiday package trip we asked a stewardess whether it would be possible for her (15yo, glider pilot...) to see the cockpit. The pilot agreed, she sat in the P1 seat and, with the seat almost but not quite fully forward she could reach the pedals (but she didn't try to move them).
However, I suspect without any evidence, that airline pilots need to be forceful individuals that can inspire everybody else to do what's necessary by their personality and demeanour. Being short, rightly or wrongly, is not a good start for that; but having a "Napoleon complex" might mitigate it!
Another obvious point is that your son's interests and abilities will change between now and then; I'm sure you know that, even if he doesn't! IMNSHO it is best to stay general for as long as possible so that he hasn't unnecessarily closed doors that he might want to go through. Also IMHO for me flying is a great hobby but I wouldn't want to do it as a job: far too boring in the long term, particularly for someone that is bright and inquisitive.
As for medical conditions, the requirements are carefully defined and are currently changing as the EASA Part-MED rules come into play. You probably don't want to see the current version at
http://hub.easa.europa.eu/crt/docs/viewnpa/id_228