A few answers to your questions...
Global Rescue is one of the best for medical evacuation when overseas. A bit pricey, but if you travel a lot they are worth it, and very comprehensive coverage. When traveling into the remotest parts of Africa, I would not go without their level of coverage. Medjet is a similar service, but not quite as good, in my opinion. I belonged to Medjet for many years. In Zim, MARS service is available for very affordable rates, but it won't get you back to the states, just to a major hospital.
Afton House has a very good reputation, but is ondergoing some management changes with the death of the original owner. Still family run, and they can take care of you. Another well respected location is African Sky Guest house, with similar services. I try to avoid staying in Joberg when possible, as I want to hunt and not stay in a major city.Look at the Gracey travel website for lodging and gun permit info.
I recently used AIr2000, Hunter's support for firearm permits in RSA. Absolutely first rate, and even better service then I expected, which is always nice.
Good luck on your trip. Sounds like you got great airfare and May is a great time to hunt RSA.
Bill