Madagascar is its own country. People live there and they have a government. They use a president, although I'm not sure what his/her name is. (A quick google search popped up the name Marc Ravalomanana.) I'm not sure about needing a permit to visit there, I think you just need a passport like with most countries. I'm pretty sure you don't need a permit.
It sounds like you're talking about the Galapagos Islands, which I've heard (although never confirmed) that you need a permit to visit them, and it's owned by Ecuador.
Sure that is his name Ravalomanana. Madagascar is considered like an african country although it is a bit far from the continent. The same culture present in Madagascar is also observed on the Reunion Isle, wich is a France territory. Over there, the culture has been mixed! That's all i can tell you. Good continuation