The handle being a separate object will mean that the shading may look off, and that it will never look connected to the body. It may not be much of an issue with a teapot but certain other models it will look bizarre.
The issue you are having with roatating the teapot has to do with it’s origin. Every object has an origin and by default when you rotate or scale the object it uses this point. Your origin is far away from your object. It should be within it, or on it’s surface. A logical place would be dead center on the bottom. This way you can scale it on a table and not have it pushing through the floor.
Select the teapot.
Tab in edit mode.
Select the single vertex on the bottom, dead center.
in the menu at the bototm, click mesh -> snap -> cursor to selected.
The 3-d cursor should move to the vertex you selected.
Tab into object mode
in the tools panel (hit t) click
‘set origin’- -> to 3-d cursor.
Now when you rotate/scale the teapot it will pivot/scale about the new origin.
Post a render of the teapot where you can clearly see the handle connected.