How deep must the shroud be to be effective?
Will a 2 bladed prop work, or will a 3 or 4 blade be more efficient?
What are the advantages to a shroud? More efficient use of the prop?

I have no idea what you are talking about. Do you mean a cowl?

A shrouded prop, kinda like a turbine.

..a ducted fan, maybe ?

The principle purpose of a shrouded prop is to eliminate the vortex ring generated at the tip of the propeller. There is a component of this ring that disturbs the airflow be hind the propeller and drops the efficiency. The trouble is that the struts needed to support the shroud cause as much negative effect as if you didn't use the shroud in the first place.. I fly a 13 foot R/C advertising blimp and the two main lift fans are shrouded. On a wood 6x3 prop I gain about a half ounce of thrust off each prop in the ducts.. In my case the shrouds primary purpose is to keep peoples fingers out of the blades