Actually, they do. The Mega Drive (or Genesis if you live in the USA) is backwards compatable. Originally, Sega released the Power Base converter in all regions. This is essentially an extention to...
The Mega Drive and Genesis are the same thing, only the mega drive in European and the genesis is American
You will need a power base converter
Yes. Sega Mega Drive is the Japanese and European name for it, while Sega Genesis is the North American name for it.
There is a game called Alien Storm for Sega Mega Drive.