What is the easiest and most cost effective way to turn a 1 bedroom apartment into 2 bedrooms?
Unless your existing room already happens to have two doors then the project that you propose is never going to get any where because the project is more than trying to build some divider wall. 

Trying to cut an additional doorway into the room is just not something you can freely do to a property that you happen to be renting.

Additionally the requirements you have placed on the performance of the divider wall would require that you build in a good solid wall. This is simply not something you can do to a property that you are renting.