I think in the newer versions of maya things like extrude face and extrude edge have just been combined into a single command "extrude" under edit mesh, and it will either extrude edges or faces depending on what is selected.

I think "merge" works for vertices, but there is also a "merge vertex tool" which you can use interactively without selecting the vertices first.

I have the append to polygon tool under my edit mesh menu, but I am using 2009, so it may have changed?

Hope that helps.