Create an object on the face of another?
 

Can I select a face and create a primitive directly on top of the face? rather than creating one and guess-timating it in the right position?

Im not sure exactly what you are trying to do. If I understand your question corectly the answer is no, I think. You can just point snap your new object into place however. To point snap just hold down the "v" key then drag. Hope that helps.

I don't think so, but once you have both objects you can snap align one of the object to a point on the surface of the other.