The Greater Middle East includes all of the countries of the Middle East plus North Africa, Afghanistan, Pakistan, Cyprus, and parts of the Horn of Africa.

If you by Georgia mean the state in the U.S. then no. But if you mean the country south of Russia, then both yes and no: It is not part of the general definition, but is a part of the Greater Middle East.

All countries have some fresh water to a greater or lesser extent.

That depends on the definition. Generally, most geographers place Afghanistan in South Asia, not in the Middle East. Additionally, the traditional definition of the Middle East doesn't include Afghanistan. However, the "Greater Middle East" includes Afghanistan.

Malaria lives in mosquito's found in greater part of Africa, Middle east, South-east Asia, and South America.