Could you help me figure out what sort of laboratory glassware apparatus this is?
I think you got a Soxhlet extractor in the diagram......
The apparatus has some sockets to attach a condenser and gas line; in the top cavity you place a thimble made out of filter paper, which is filled with solid that is to be extracted by the solvent at reflux. The solid contains insoluble material (which is retained by the thimble), and a soluble component, which is slowly extracted by the solvent at reflux.
If you really want to know, go and see a glass-blower. If there is not one in your department, go to a department that still has scientific glassblowers; they are usually very friendly and approachable.