Can you build a ship in the Caspian Sea?
Yes, there are versions of Axis and Allies that allow building ships in the Caspian Sea. This is the exception tough. In Axis and Allies 1941/1942, the Caspian Sea is not considered a sea zone and you cannot build any ships there. 

In Axis and Allies 1940 Europe/Global, the Caspian Sea is a sea zone. Therefore, you can build ships there.