3. Much as I know pilots have places they can divert to in the case of technical emergencies do they have similar locations for medical emergencies.
If I may add to Airbus Girl's comprehensive answer, and adding a Longhaul perspective.
The Medical provider will provide guidance as to where to go, and on a longhaul flight that may
not be where you would choose to go with a technical problem. For example whilst over the Western Atlantic if you had a technical problem the nearest suitable runway might be at Gander, but the best hospital (as I understand it) might be at St. Johns, so the medical provider may well suggest overflying Gander and going direct to St. John's.