First of all there is no plane from Madinah to Makkah. Makkah doesn't have an airport. I hear there's a new high speed train you may want to look into. Otherwise you will be going by road or flying to Taif or Jeddah first and then by road. As for your flight that lands at 7 am at the South Terminal, you appear to be saying it will be a domestic flight. Therefore you won't have any immigration.
Also be aware that Jeddah is soft opening a new terminal. Over a period of months they are slowly transferring domestic flights to the new terminal. In fact there's a Saudi Gazette article that says that Madinah flights will soon use this new terminal. So make sure you find out where your flight is going.
As for South to North Terminal transfers, I used to do this. It's one of the most irritating, frustrating airport setups in the world. The two terminals are physically only about 1 km apart. But any transfer between the two requires a road transfer of about 19 km. You have to go way around. My last time to do this was about 4 years ago so this information could be dated. Taxi drivers will try to shamelessly rip you off. They will ask something like 200 SAR and they will bargain hard. They will also insist that there is no shuttle bus, whether there is or not. If you can get them down to 100 you are doing well.
I have used a shuttle bus there. But, perhaps intentionally, it isn't easy to find. When I was using it, it was a white minibus that was parked to the right of the exit from the South Terminal and past the first turn. I think they charged something like 30 SAR. It only left something like once an hour. I can't say whether it's still there or not. Good luck.